signal processing using scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...introduction...
TRANSCRIPT
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Signal Processing Using Scilab
Manas DasIndian Institute of Technology, Bombay
February 21, 2012
![Page 2: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/2.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse functionStep functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 3: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/3.jpg)
Introduction
Signal Basics
What is signal?
Different types of signal
Impulse functionStep functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 4: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/4.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse functionStep functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 5: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/5.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse function
Step functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 6: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/6.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse functionStep function
Ramp function
Manas Das, IITB Signal Processing Using Scilab
![Page 7: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/7.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse functionStep functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 8: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/8.jpg)
Introduction
Signal Basics
What is signal?Different types of signal
Impulse functionStep functionRamp function
Manas Das, IITB Signal Processing Using Scilab
![Page 9: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/9.jpg)
Linear Time-Invariant Systems
Convolution
Continuous time convolution
Discrete time convolution
Circular convolution
Correlation
Manas Das, IITB Signal Processing Using Scilab
![Page 10: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/10.jpg)
Linear Time-Invariant Systems
Convolution
Continuous time convolution
Discrete time convolution
Circular convolution
Correlation
Manas Das, IITB Signal Processing Using Scilab
![Page 11: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/11.jpg)
Linear Time-Invariant Systems
Convolution
Continuous time convolution
Discrete time convolution
Circular convolution
Correlation
Manas Das, IITB Signal Processing Using Scilab
![Page 12: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/12.jpg)
Linear Time-Invariant Systems
Convolution
Continuous time convolution
Discrete time convolution
Circular convolution
Correlation
Manas Das, IITB Signal Processing Using Scilab
![Page 13: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/13.jpg)
Linear Time-Invariant Systems
Convolution
Continuous time convolution
Discrete time convolution
Circular convolution
Correlation
Manas Das, IITB Signal Processing Using Scilab
![Page 14: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/14.jpg)
Different types of Transform
Fourier Transform
Laplace Transform
Z-Transform
Manas Das, IITB Signal Processing Using Scilab
![Page 15: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/15.jpg)
Different types of Transform
Fourier Transform
Laplace Transform
Z-Transform
Manas Das, IITB Signal Processing Using Scilab
![Page 16: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/16.jpg)
Different types of Transform
Fourier Transform
Laplace Transform
Z-Transform
Manas Das, IITB Signal Processing Using Scilab
![Page 17: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/17.jpg)
Different types of Transform
Fourier Transform
Laplace Transform
Z-Transform
Manas Das, IITB Signal Processing Using Scilab
![Page 18: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/18.jpg)
Fourier Transform
A mathematical operation that converts signal fromtime domain to its frequency domain
Fourier Transform of continuous time signal
Fourier Transform of Discrete time signalDiscrete Fourier Transform (DFT)Fast Fourier Transform(FFT)
Manas Das, IITB Signal Processing Using Scilab
![Page 19: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/19.jpg)
Fourier Transform
A mathematical operation that converts signal fromtime domain to its frequency domain
Fourier Transform of continuous time signal
Fourier Transform of Discrete time signalDiscrete Fourier Transform (DFT)Fast Fourier Transform(FFT)
Manas Das, IITB Signal Processing Using Scilab
![Page 20: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/20.jpg)
Fourier Transform
A mathematical operation that converts signal fromtime domain to its frequency domain
Fourier Transform of continuous time signal
Fourier Transform of Discrete time signal
Discrete Fourier Transform (DFT)Fast Fourier Transform(FFT)
Manas Das, IITB Signal Processing Using Scilab
![Page 21: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/21.jpg)
Fourier Transform
A mathematical operation that converts signal fromtime domain to its frequency domain
Fourier Transform of continuous time signal
Fourier Transform of Discrete time signalDiscrete Fourier Transform (DFT)Fast Fourier Transform(FFT)
Manas Das, IITB Signal Processing Using Scilab
![Page 22: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/22.jpg)
DFT
Discrete Fourier transform
Calling Sequence[xf]=dft(x,flag);
x :input vector
flag: indicates dft (flag=-1) or idft (flag=1)
xf: output vector
Manas Das, IITB Signal Processing Using Scilab
![Page 23: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/23.jpg)
DFT
Discrete Fourier transformCalling Sequence[xf]=dft(x,flag);
x :input vector
flag: indicates dft (flag=-1) or idft (flag=1)
xf: output vector
Manas Das, IITB Signal Processing Using Scilab
![Page 24: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/24.jpg)
DFT
Discrete Fourier transformCalling Sequence[xf]=dft(x,flag);
x :input vector
flag: indicates dft (flag=-1) or idft (flag=1)
xf: output vector
Manas Das, IITB Signal Processing Using Scilab
![Page 25: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/25.jpg)
DFT
Discrete Fourier transformCalling Sequence[xf]=dft(x,flag);
x :input vector
flag: indicates dft (flag=-1) or idft (flag=1)
xf: output vector
Manas Das, IITB Signal Processing Using Scilab
![Page 26: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/26.jpg)
DFT
Discrete Fourier transformCalling Sequence[xf]=dft(x,flag);
x :input vector
flag: indicates dft (flag=-1) or idft (flag=1)
xf: output vector
Manas Das, IITB Signal Processing Using Scilab
![Page 27: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/27.jpg)
FFT
Fast Fourier transform
Calling Sequence[x]=fft(a);
x :real or complex vector
a: real or complex vector, matrix ormultidimensional array.
Manas Das, IITB Signal Processing Using Scilab
![Page 28: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/28.jpg)
FFT
Fast Fourier transformCalling Sequence[x]=fft(a);
x :real or complex vector
a: real or complex vector, matrix ormultidimensional array.
Manas Das, IITB Signal Processing Using Scilab
![Page 29: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/29.jpg)
FFT
Fast Fourier transformCalling Sequence[x]=fft(a);
x :real or complex vector
a: real or complex vector, matrix ormultidimensional array.
Manas Das, IITB Signal Processing Using Scilab
![Page 30: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/30.jpg)
FFT
Fast Fourier transformCalling Sequence[x]=fft(a);
x :real or complex vector
a: real or complex vector, matrix ormultidimensional array.
Manas Das, IITB Signal Processing Using Scilab
![Page 31: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/31.jpg)
Laplace Transform
A linear operator of a function f(t) with a real argument t (t=0)that transforms it to a function F(s) with a complex argument s
Manas Das, IITB Signal Processing Using Scilab
![Page 32: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/32.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 33: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/33.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 34: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/34.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 35: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/35.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 36: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/36.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 37: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/37.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 38: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/38.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 39: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/39.jpg)
z-Transform
Calling Sequence[czx]=czt(x,m,w,phi,a,theta)Arguements
x :input data sequence
m: czt is evaluated at m points in z-plane
w:magnitude multiplier
phi: phase increment
a:initial magnitude
theta:initial phase
czx:chirp z-transform output
Manas Das, IITB Signal Processing Using Scilab
![Page 40: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/40.jpg)
Sampling
Nyquist Criteria
An analog signal that has been sampled can beperfectly reconstructed from an infinite sequenceof samples if the sampling rate exceeds 2Bsamples per second, where B is the highestfrequency of the original signal
AliasingAmbiguity from reconstructionShannon-Nyquist Sampling theoremUnder-sampling
Manas Das, IITB Signal Processing Using Scilab
![Page 41: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/41.jpg)
Sampling
Nyquist CriteriaAn analog signal that has been sampled can beperfectly reconstructed from an infinite sequenceof samples if the sampling rate exceeds 2Bsamples per second, where B is the highestfrequency of the original signal
Aliasing
Ambiguity from reconstructionShannon-Nyquist Sampling theoremUnder-sampling
Manas Das, IITB Signal Processing Using Scilab
![Page 42: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/42.jpg)
Sampling
Nyquist CriteriaAn analog signal that has been sampled can beperfectly reconstructed from an infinite sequenceof samples if the sampling rate exceeds 2Bsamples per second, where B is the highestfrequency of the original signal
AliasingAmbiguity from reconstruction
Shannon-Nyquist Sampling theoremUnder-sampling
Manas Das, IITB Signal Processing Using Scilab
![Page 43: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/43.jpg)
Sampling
Nyquist CriteriaAn analog signal that has been sampled can beperfectly reconstructed from an infinite sequenceof samples if the sampling rate exceeds 2Bsamples per second, where B is the highestfrequency of the original signal
AliasingAmbiguity from reconstructionShannon-Nyquist Sampling theorem
Under-sampling
Manas Das, IITB Signal Processing Using Scilab
![Page 44: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/44.jpg)
Sampling
Nyquist CriteriaAn analog signal that has been sampled can beperfectly reconstructed from an infinite sequenceof samples if the sampling rate exceeds 2Bsamples per second, where B is the highestfrequency of the original signal
AliasingAmbiguity from reconstructionShannon-Nyquist Sampling theoremUnder-sampling
Manas Das, IITB Signal Processing Using Scilab
![Page 45: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/45.jpg)
FIR Filter Equation
FIR Filters are represented as:-
H(z) =N∑
k=0
hkZ−k (1)
Manas Das, IITB Signal Processing Using Scilab
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Window Functions for FIR Filter Design
Hamming Window
win hamming=window(’hm’,n)
Kaiser Windowwin kaiser=window(’kr’,n,alpha)
Chebyshev Windowwin chebyshev=window(’ch’,n,par)
Manas Das, IITB Signal Processing Using Scilab
![Page 47: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/47.jpg)
Window Functions for FIR Filter Design
Hamming Windowwin hamming=window(’hm’,n)
Kaiser Window
win kaiser=window(’kr’,n,alpha)
Chebyshev Windowwin chebyshev=window(’ch’,n,par)
Manas Das, IITB Signal Processing Using Scilab
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Window Functions for FIR Filter Design
Hamming Windowwin hamming=window(’hm’,n)
Kaiser Windowwin kaiser=window(’kr’,n,alpha)
Chebyshev Window
win chebyshev=window(’ch’,n,par)
Manas Das, IITB Signal Processing Using Scilab
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Window Functions for FIR Filter Design
Hamming Windowwin hamming=window(’hm’,n)
Kaiser Windowwin kaiser=window(’kr’,n,alpha)
Chebyshev Windowwin chebyshev=window(’ch’,n,par)
Manas Das, IITB Signal Processing Using Scilab
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Window based Linear Phase FIR filter
Calling Sequence[wft,wfm,fr]=wfir(ftype,forder,cfreq,wtype,fpar)Arguments
ftype: ’lp’,’hp’,’bp’,’sb’ (filter type)
wtype: Window type(’re’,’tr’,’hm’,’hn’,’kr’,’ch’)
wft: time domain filter coefficients
wfm: frequency domain filter response on thegrid fr
fr: Frequency grid
Manas Das, IITB Signal Processing Using Scilab
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Window based Linear Phase FIR filter
Calling Sequence[wft,wfm,fr]=wfir(ftype,forder,cfreq,wtype,fpar)Arguments
ftype: ’lp’,’hp’,’bp’,’sb’ (filter type)
wtype: Window type(’re’,’tr’,’hm’,’hn’,’kr’,’ch’)
wft: time domain filter coefficients
wfm: frequency domain filter response on thegrid fr
fr: Frequency grid
Manas Das, IITB Signal Processing Using Scilab
![Page 52: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/52.jpg)
Window based Linear Phase FIR filter
Calling Sequence[wft,wfm,fr]=wfir(ftype,forder,cfreq,wtype,fpar)Arguments
ftype: ’lp’,’hp’,’bp’,’sb’ (filter type)
wtype: Window type(’re’,’tr’,’hm’,’hn’,’kr’,’ch’)
wft: time domain filter coefficients
wfm: frequency domain filter response on thegrid fr
fr: Frequency grid
Manas Das, IITB Signal Processing Using Scilab
![Page 53: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/53.jpg)
Window based Linear Phase FIR filter
Calling Sequence[wft,wfm,fr]=wfir(ftype,forder,cfreq,wtype,fpar)Arguments
ftype: ’lp’,’hp’,’bp’,’sb’ (filter type)
wtype: Window type(’re’,’tr’,’hm’,’hn’,’kr’,’ch’)
wft: time domain filter coefficients
wfm: frequency domain filter response on thegrid fr
fr: Frequency grid
Manas Das, IITB Signal Processing Using Scilab
![Page 54: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/54.jpg)
Window based Linear Phase FIR filter
Calling Sequence[wft,wfm,fr]=wfir(ftype,forder,cfreq,wtype,fpar)Arguments
ftype: ’lp’,’hp’,’bp’,’sb’ (filter type)
wtype: Window type(’re’,’tr’,’hm’,’hn’,’kr’,’ch’)
wft: time domain filter coefficients
wfm: frequency domain filter response on thegrid fr
fr: Frequency grid
Manas Das, IITB Signal Processing Using Scilab
![Page 55: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/55.jpg)
Equiripple FIR Filter Design
Calling Sequence[hn]=eqfir(nf,bedge,des,wate)Arguments
nf: number of output filter points desired
bedge: Mx2 matrix giving a pair of edges foreach band
des: M-vector giving desired magnitude for eachband
wate: M-vector giving relative weight of errorin each band
hn: output of linear-phase FIR filtercoefficients
Manas Das, IITB Signal Processing Using Scilab
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Equiripple FIR Filter Design
Calling Sequence[hn]=eqfir(nf,bedge,des,wate)Arguments
nf: number of output filter points desired
bedge: Mx2 matrix giving a pair of edges foreach band
des: M-vector giving desired magnitude for eachband
wate: M-vector giving relative weight of errorin each band
hn: output of linear-phase FIR filtercoefficients
Manas Das, IITB Signal Processing Using Scilab
![Page 57: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/57.jpg)
Equiripple FIR Filter Design
Calling Sequence[hn]=eqfir(nf,bedge,des,wate)Arguments
nf: number of output filter points desired
bedge: Mx2 matrix giving a pair of edges foreach band
des: M-vector giving desired magnitude for eachband
wate: M-vector giving relative weight of errorin each band
hn: output of linear-phase FIR filtercoefficients
Manas Das, IITB Signal Processing Using Scilab
![Page 58: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/58.jpg)
Equiripple FIR Filter Design
Calling Sequence[hn]=eqfir(nf,bedge,des,wate)Arguments
nf: number of output filter points desired
bedge: Mx2 matrix giving a pair of edges foreach band
des: M-vector giving desired magnitude for eachband
wate: M-vector giving relative weight of errorin each band
hn: output of linear-phase FIR filtercoefficients
Manas Das, IITB Signal Processing Using Scilab
![Page 59: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/59.jpg)
Equiripple FIR Filter Design
Calling Sequence[hn]=eqfir(nf,bedge,des,wate)Arguments
nf: number of output filter points desired
bedge: Mx2 matrix giving a pair of edges foreach band
des: M-vector giving desired magnitude for eachband
wate: M-vector giving relative weight of errorin each band
hn: output of linear-phase FIR filtercoefficients
Manas Das, IITB Signal Processing Using Scilab
![Page 60: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/60.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 61: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/61.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 62: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/62.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 63: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/63.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 64: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/64.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 65: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/65.jpg)
IIR Digitalfilter
Calling Sequence[hz]=iir(n,ftype,fdesign,frq,delta)Arguments
n:the filter order
ftype:filter type,lp’ for low-pass,’hp’ for highpass,’bp’ for band pass and ’sb’ for stop band
fdesign:the analog filter design, the possiblevalues are: ’butt’, ’cheb1’, ’cheb2’ and ’ellip’
frq:2-vector of discrete cut-off frequencies(i.e., 0<frq<.5). For ’lp’ and ’hp’ filters onlyfrq(1) is used. For ’bp’ and ’sb’ filters frq(1)is the lower cut-off frequency and frq(2) is theupper cut-off frequency
delta: 2-vector of error values
Manas Das, IITB Signal Processing Using Scilab
![Page 66: Signal Processing Using Scilabfileexchange.scilab.org/toolboxes/219000/1.0/files/...Introduction Signal Basics What is signal? Di erent types of signal Impulse function Step function](https://reader031.vdocument.in/reader031/viewer/2022022012/5b24a7ba7f8b9a59098b45b7/html5/thumbnails/66.jpg)
Filter
To design filter of any magnitudeFunction- fremezb
¯Calling Sequencean=remezb(nc,fg,ds,wt)
nc: half-filter length
fg: dense grid of frequency
s: derived magnitude values on this grid
wt: error weighting vectors
an: filter coeffficients
Manas Das, IITB Signal Processing Using Scilab
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Filter
Filtering of discrete signals by flts functionFunction- fltsCalling Sequencey,[x]=flts(u,s1[,x0])
u: hte data to be filtered
x0: initial state vector/matrix giving necessaty i/p-o/p.itallows for filtering of length signals
x: optimal variable which givesh the state sequence.
Manas Das, IITB Signal Processing Using Scilab
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Textbook Companion
You already know Textbook Companion Project
There are books on Signal Processing using Scilab under thisproject
Refer to the link: http://www.scilab.in/Completed Books
Manas Das, IITB Signal Processing Using Scilab
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Textbook Companion
You already know Textbook Companion Project
There are books on Signal Processing using Scilab under thisproject
Refer to the link: http://www.scilab.in/Completed Books
Manas Das, IITB Signal Processing Using Scilab