a dsp sample problems

Sample QuestionsAdvanced Digital Signal Processing

Question Draw the butterfly structure and compute all the values on all the intermediate nodes while computing 4-point FFT of a signal x[n]=[a 0 0 0]

Question Use triangular window to design a causal FIR filter of length 5 and cutoff frequency ωc=π/3, Plot the coefficients of the filter

Question Given 5 point circular convolution of two sequences x[n] and h[n] of length 3 and 3 as y[n] = [8 0 4 12],if x[n] = [1 2 3], find all the possible samples of h[n].

Question For the following two sequences

Determine and sketch 100-point Circular convolution of two sequences.

QuestionFor the following analog response of a filter

a) Find the impulse response of the equivalent Discrete-Time system using bilinear Transformation.

b) Is the Discrete System Low-pass or High-pass? Give rational.

Question of Figure 1 is input to system shown in Figure 2, plot Fourier Transform of signal

at the output of each block of the system for and

2π400

1

Ω2π800-2π800

1

-2π400

Figure 1:

Question Answer the following:

a. Draw magnitude of the frequency response of an ideal Low-pass and Band-stop filters.

b. Compute 4-point DFT of

Question

Answer the following a. Use bit reverse addressing to generate indices of first four input data values for

computing 1024 point FFT of a discrete time signal b. A four point periodic sequence and its DFS are given

and

Compute the DFS of c. Compute the linear convolution of two sequences and of lengths

, 6-point circular convolution and first samples of both the signals are given as , and respectively.

Question Answer the following:

1) Split the signal into L and H components using Haar Wavelets. Re compute the original signal from the two components.

2) Mother wavelet is shown in figure below, draw a drived wavelet

for and

Question Answer the following

a. In a decimation in time 4-point FFT computation, 2-points FFTs are

ADC DAC

T1 T2

Compute b. The 4-point Circular convolution of two 4-point signals is given

as

If find 4-point circular convolution

of the three signals .

QuestionAnswer the following:

1) Derived wavelet for and is given below, draw the mother

wavelet. 2) An interpolation filter for L = 5 has an impulse response of

Draw the poly-phase structure of the filter and compute 1st and 5th interpolated output sample for