JRE SCHOOL OF Engineering

CLASS TEST-1 EXAMINATIONS MARCH 15

Subject Name Digital Signal Processing

Subject Code EEC 602

Roll No. of Student Max Marks 30Max Duration 1 Hr

Date 13 MARCH 2015 Time 9:20 AM-10:20 AMFor ECE & AEI branches only

SECTION – A (3 marks * 5 Questions = 15 Marks)

Attempt any five:1) Compare DFT with DTFT.Soln. I) DFT is defined for finite number of sequences while DTFT is defined for any arbiturary sequences.ii) DFT is expressed as:

while DTFT is expressed as:

iii)DFT is faster computational technique as compared to DTFT.

2) For the sequence x(n)={0,1,2,3}, find (a) x((n-2))4, and (b) x((-n))4.Soln.

3) Compute 4-point DFT of causal three sample sequence given by:

Soln. By definition of N-point DFT, the kth is complex co-efficient of X (k) for

is given by

X ( k )=∑n=0

N−1

x (n)W Nnk

X [k ]= ∑n=−∞

∞

x [n ]e− jωn

Here N = 4, therefore the 4-point DFT is

The values of X (k) can be evaluated for k = 0, 1, 2, 3.

4) Explain in detail all basic elements of DSP.

Soln.The basic elements of digital signal processing system are shown in fig. below

The different blocks of this system as follows.1 I/P Signal: It is the signal generated from some transducer or from some communication system It may be biomedical signal like ECG or EEC. Generally input signal is analog in nature It is denoted as x(t).2. Anti Aliasing filter: It is basically a low pass filter. It is used for the following purposes.(a) It removes the high frequency noise contain in input signal.(b) It avoids aliasing effect that means it is used to band limit the signal.3. Sample and Hold circuit. It takes samples of I/P signal. It keeps the voltage level of I/P signal relatively constant which is the requirement of ADC.4 Analog to digital converter (ADC): It is used to convert analog signal into digital form. This is required because digital signal processor accepts the signal which is digital in nature.5. Digital Signal Processor: It processes input signal digitally. It modifies the signal as per requirement . For this purpose DSP processors like ADSP 2100 or TMS 320 are used.6 Digital to analog converter (DAC): The output of digital signal processor is digital in nature. But the required final output is analog in nature. So to convert digital signal into analog signal DAC is used.7 Reconstruction Filter: Output signal of DAC is analog that means it is continuous signal. But it may contain high frequency components. Such high frequency components are unwanted. To remove these components reconstruction filter is used.

5) The first six points of the 8-point DFT of a real valued sequence are { 0.25, -j0.3018,0,0,0.125,-j0.0518}.Determine the remaining points.

Soln.X(0)= 0.25, X(1)= -j0.3018, X(2)=0, X(3)=0,X(4)= 0.125, X(5)= -j0.0518

X*(k)=X(N-k)

Therefore, X(k)=X*(N-k)= X*(8-k)

X(6)= X*(8-6)= X*(2)=0

X(7)= X*(8-7)= X*(1)= j0.3018

6) Find the inverse DFT of X(k) = {1, 2, 3, 4}.

Soln.

SECTION – B (5 marks * 1 Questions = 5 Marks)

1) Determine the linear convolution of the given sequences and compare the result by performing 8 point circular convolution of two sequences:

Soln.Linear convolution and circular convolution using matrix method is

OR2) A four point sequence x(n)={1,2,3,4} has DFT X(k), 0≤k≤3.Without

performing DFT or IDFT, determine the signal values which has DFT X(k-1).Soln.

SECTION – C (10 marks * 1 Questions = 10 marks)

1) By means of the DFT & IDFT, determine the sequence x3 (n) corresponding to the circular convolution of the sequence x1 (n) and x2(n).

Soln. First we compute the DFT’s of x1 (n) and x2(n). The four point DFT of x1 (n) is

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