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PendahuluanAnalisis Spektrum Sinyal Digital
Oleh :Herlan Darmawan
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Pendahuluan
• Kontrak kuliah :• 1. absensi : 25%• 2. tugas : 25%• 3. mid : 25%• 4. uas :25%
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Pendahuluan
• Why geophysicist/physicist needs to learn “ASSD”?
• What is signal?• What is spectrum?
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Why geophysicist needs to learn ASSD
• We deal with geophysical data such as potential field data (gravity, magnetic, or electrical survey).
• That potential data are displayed mostly in 1D (profile form), 2D (map form), or 3D (map and depth display) spatial data.
• When data express thematic value (magnitude vs space /thematic value vs time), it is called time series data or time domain data.
• Time domain data are poor and undiscernable possibly because of noise effects and other measurement errors.
• We need to understand signal processing and signal analysis.
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What is signal ??
• A signal is a function of one or more variable as a function of time.
• Signal can be divided :• Continuous-time signal• Discrete-time signal• Periodic signal• Non-periodic signal• Even and odd signal• Exponensial signal
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Continuous-time signal
• It is also called an analog signal, defined on the continuum of time values (if the independent variable (t) is continuous) . Example of continuous – time signal :
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Discrete-time signal
• A discrete – time signal is defined at discrete times (if the independent variable (t) takes only in discrete values, ex t : ±1, ±2, ±3, etc). It is called a digital signal if its amplitude is quantized to a series of discrete levels.
Discrete time signal Digital signal
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Periodic signal
• A continuous – time signal x(t) is periodic with period T, if : x(t+T)=x(t).
• Periodic signal has same wave-shape every T seconds and infinitely often
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Non-periodic signal
• Signal that do not repeat at regular intervals
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Even and odd signal
• One of the characteristics of signal is symmetry that may be useful for signal analysis. Even signals are symmetric around vertical axis, and odd signal are symmetric about origin.
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Exponential signal
• f(t) = 1 (t).A• If α > 0 then is exponentially increasing• If α < 0 then is exponentially decreasing, and• If α = 0 then =1, means the step signal 1(t)
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What is spectrum ?
• The spectrum of a signal is a detailed description of the frequency components the signal contains.
• Spectrum analysis also referred to as frequency domain analysis or spectral density estimation.
• The frequency spectrum can be generated via fourier transform.
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Introduction to system
• A system is a device which converts an input signal (excitation) into an output signal (response).
• A continuous-time system : input & output are continuous signal
• A discrete-time system : system whose input and output are discrete-time signals.
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System classification
• Linear system• When the input is a weighted sum of several inputs,
the output will be the weighted sum of the corresponding inputs. Otherwise, the sistem is nonlinear.
• X1(t) and x2(t) are 2 arbitrary signal, a1 and a2 are two arbitrary constants. System y(t)=T[x(t)] is linear if :
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Time-invariant vs time variant systems
• Time invariant system : input signal has a time shift, So the output?. Otherwise, the system is variant
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Time shift??
• One of the CT signals operation• Y(t) = x(t-td)• Shift the origin of the signal to td• Ex : y(t) = u(t-2)
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Signal operations
• Time reversal y(t) = x(-t)• Time shifting y(t)=x(t-td)• Amplitude scaling y(t) = Bx(t)• Addition y(t)=x1(t) + x2(t)• Multiplication y(t)=x1(t).x2(t)• Time scaling y(t)=x(at)
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Time reversal
• Flips the signal about the y axis y(t) = x(-t)• Ex : x(t) = u(t), y(t)=u(-t)• Let “a” be the argument of the step function u(a)
• Let a = -t and plug this value of “a”
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Amplitude scaling
• Multiply the entire signal by a constant value• Y(t) = Bx(t)• Sketch y(t)=5u(t)
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Addition of signals
• Point-by-point addition of multiple signals• Move from the left to right (/vice versa) and add the value of
each signal together to achieve the final signal• Y(t)=x1(t) + x2(t)• Ex : skecth y(t) = u(t) – u(t-2)• First, plot each of the portions of this signal separately• X1(t) = u(t)• X2(t)=-u(t-1)• Then, move from one side • To other and add their• Instantaneous values
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Multiplication of signals
• Point-by-point multiplication of the values• Ex : skecth y(t) = u(t).u(t-2)• Skecth it separately then move from one side
to other, and multiply instantaneous values
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Time scaling
• Speed up or slow down a signal• Y(t) = x (at)• |a| > 1 speed up x(t) by factor “a”• |a| < 1 slow down x(t) by factor “a”
• Ex : x(t) = u(t) – u(t-2)• Sketch y(t) = x(2t)• Replace all t’s with 2t• Y(t) = x(2t) = u(2t) – u(2t-2)
• (what occured at t=2 now occurs at t=2/2=1)
First, plot x(t)
Turns on at
No change
Turns on at