## Digital Signal Processing MCQ1) The product of two odd signals is: - Odd
- Even
- Both (a) and (b)
- Zero
If both these signals are odd, x1(-n) = - x1(n) and x2(-n) = - x2(n) If a signal is even, x(-n) = x(n) x(-n) = x1(-n) . x2(-n) x(-n) = - x1(n). - x2(n) x(-n) = x1(n). x2(n) It means that x(-n) = x(n), which is even. Hence, the product of two odd signals is even. 2) The system given by y(n) = x(n) + 1/x(n - 1) is: - Linear
- Causal
- Both (a) and (b)
- None of the above
We will check the value of y(n) for different values of n. For, n= 0, y(0) = x(0) + 1/x(-1) n = 1, y(1) = x(1) + 1/x(0) Thus, the system is causal.
Y1(n) = x1(n) + 1/x1(n - 1) Y2(n) = x2(n) + 1/x2(n - 1) To satisfy the linearity, ay1(n) + by2(n) = ax1(n) + bx2(n) LHS ay1(n) + by2(n) = a [x1(n) + 1/x1(n - 1)] + b [x2(n) + 1/x2(n - 1)] ay1(n) + by2(n) = ax1(n) + bx2(n) + a/x1(n - 1) + b/x2(n - 1) It is not equal to RHS Hence, the system is non-linear. 3) Which of the following is not a type of discrete system? - Recursive systems
- Dynamic systems
- Non-causal systems
- Non-dynamic systems
4) The advantages of discrete signal processing is/are: - Cost effective
- Time sharing
- High flexibility
- All of the above
5) Which of the following is the characteristic of the power signal? - Power signal is infinite.
- Power signals are time-limited.
- Aperiodic signals are power signals.
- None of the above
6) The Digital Signal Processing system: - Consumers more power.
- Consumes less power.
- Applicable for low-frequency signals.
- Both (a) and (c).
7) The length of the output sequence (n) of the two sequences (n1 and n2) can be calculated using the formula: - n = n1 - n2 + 1
- n = n1 + n2 - 1
- n = n1 - n2 - 1
- n = n1 + n2 + 1
If, n1 = 4 and n2 = 3, n = 4 + 3 - 1 = 6 8) An analog signal has a bandwidth of 5KHz. If we are using an N-point DFT to compute the signal spectrum with a resolution less than or equal to 25Hz. Find the minimum length of the signal. - 0.2s
- 0.04s
- 0.02s
- 0s
N = 2^m, where m is the integer Minimum length of the signal (T) is given by: T = L/Fs Where, L is the minimum number of requires samples Fs is the minimum sampling rate Fs = 2fm It means that the sampling rate is twice the bandwidth. Fs = 2 x 5 = 10 KHz. L = Fs/Resolution So, T = (Fs/ Resolution)/ Fs T = 1/Fs T = 1/25Hz T = 0.04s 9) One-sided Z-transform is also known as: - Unilateral Z-transform
- Bilateral Z-transform
- Trilateral Z-transform
- None of the above
10) The Z-transform of the function y(n) = x(n) + y(n - 1) is: - z/ z + 1
- z/ 2z
- z/ z - 1
- z - 1/z
Applying Z-transform on both the sides, Z [y(n)] = Z [x(n)] + Z y[(n - 1)] Y(z) = X(z) + z^(-1) Y(z) Y(z) - z^(-1) Y(z) = X(z) Y(z) (1 - 1/z) = X(z) Y(z) (1 - 1/z) = X(z) Y(z)/X(z) = 1/ (1 - 1/z) H(z) = z / z-1 Thus, the Z-transform of the function y(n) = x(n) + y(n - 1) is z / z-1, which is option (c). 11) The z-transform of the signal a^nx(n) is: - X(za)
- X(z/a)
- X(z + a/a)
- None of the above
12) The z-transform of the impulse response y(n) = x(n) + 2x(n - 1) is: - 1 + 2z^-1
- 1 + 2z^2
- 1 - 2z
- 1/2z
Z [y(n)] = Z [x(n)] + Z [2x(n - 1)] Y(z) = X(z) + 2z^-1X(z) Y(z) = X(z) (1 + 2z^-1) Y(z)/X(z) = 1 + 2z^-1 H(z) = 1 + 2z^-1 13) The addition of zeroes at the end of the sequence when it is represented as the power of integer is refer as: - Region of Convergence
- Bilateral transform
- Zero padding
- None of the above
14) The z-transform of the system h(n) = 3^n u(n) is: - 3z/z - 3
- z / z + 3
- z / z + 3
- z / z - 3
So, H(z) = 1/(1 - 3/z) H(z) = z/ z - 3 Hence, z-transform of the system h(n) = 3^n u(n) is z/ z - 3. 15) The system that accepts the input in the discrete form and produces the discrete time output is known as: - Linear system
- Discrete time system
- LTI system
- All of the above
16) Find the number of smallest DFTs required to compute the linear convolution of length 40 sequences with a length of 900 another sequences using 64 DFT. - 36
- 64
- 54
- 28
M = 40 N = 900 Number of DFT = 64 The number of smaller DTS required = L + M - 1 = Number of given DFT points L + M - 1 = 64 L + 40 - 1 = 64 L = 25 Total blocks = N / L = 900/25 = 36 Hence, the number of smallest DFTs required to compute the linear convolution is 36. 17) Determine the number of complex additions required for 32 direct computations of DFT. - 240
- 56
- 992
- 854
Where, N is the number of direct DFT computations Here, N is 32. So, complex additions = 32 (32 - 1) = 32 x 31 = 992 18) Find the complex multiplications required for 16 direct computations of DFT. - 256
- 64
- 216
- 1024
Where, N is the number of direct DFT computations Here, N is 16. So, complex multiplications = 16 x 16 = 256. 19) Which of the following statement is incorrect about DIT- FFT? - It requires complex additions of 'N log2N.'
- The number of input samples is given by 2^i.
- The input sequence is represented in bit-reversal order.
- The output sequence is represented in bit-reversal order.
20) Which of the following statement is/are correct about linear convolution? 1. The Input and output sequence is Aperiodic. 2. It requires zero padding. 3. The length of the input and output sequence is the same. 4. The length of output sequence is greater than the input sequence. - Only 1
- 1 and 2
- 1 and 4
- 1, 2, 3, and 4
21) IDFT of the sequence {1, 0, 1, 0} is: - {1, 0, 0, 1}
- {0.5, 0, 0.5, 0}
- {0.5, 1, 0.5, 0}
- None of the above
x(n) = IDFT [X(k)]
x(0) = ¼ [ x(0) + x(1) + x(2) + x(3)] = ¼[1 + 0 + 1 + 0] = 2/4 = 1/2 = 0.5
x(1) = ¼ [ x(0) + x(1) + x(2) + x(3)] = ¼[1 + 0(j)+ 1(-1) + 0(-j)] = ¼ [1 +0 -1 + 0] = 0
x(2) = ¼ [ x(0) + x(1) + x(2) + x(3)] = ¼[1 + 0(-1)+ 1(1) + 0(-1)] = ¼[1 + 0 + 1 + 0] = 2/4 = 1/2 = 0.5
x(3) = ¼ [ x(0) + x(1) + x(2) + x(3)] = ¼[1 + 0(-j)+ 1(-1) + 0(j)] = ¼ [1 +0 - 1 + 0] = 0 Thus, x(n) = {0.5, 0, 0.5, 0} 22) The algorithm used for the computation of DFT based on the decomposition of N-point DFT is known as: - Overlap save
- Phase algorithm
- Divide and Conquer
- Both (a) and (b)
23) The formula to calculate the complex additions in the case of the divide and conquer approach is: - N (M + L - 1)
- N (M - L + 1)
- N (M + L + 3)
- N (M + L - 2)
Where, M and L are the integers of the given data array, and N is the number point DFT. The number of complex additions for the above approach is less than the direct form approach. 24) Determine the number of complex multiplications for the 8-point Radix-2 FET. - 32
- 12
- 80
- 4
Where, N is the point DFT. Thus, the complex multiplications = 8/2 (log2 8) = 4 x 3 = 12. 25) The advantages of the butterfly structure is: - Reduces computation complexity.
- Requires a fewer number of multiplications and additions.
- Combines the result of small DFTs into larger DFTs.
- All of the above
26) Which of the following is/are incorrect about the Cascade realization of the IIR systems? - It requires less amount of energy.
- It is helpful in determining the overall transfer function.
- The filters in the cascade are connected in parallel.
- None of the above
27) Linear phase response of the filter is defined as: - When the phase response of the system varies linearly with the frequency function.
- When the phase response of the system varies inversely with the frequency function.
- When the phase response of the system does not vary linearly with the frequency function.
- None of the above.
28) Which of the following statement is/are incorrect about the FIR filters? 1. FIR filters are always stable. 2. It requires more memory as compared to IIR filters. 3. FIR filters are non-canonical. 4. Its linear phase realization structure can be easily designed. - 1 and 2
- Only 2
- Only 3
- 3 and 4
29) Digital filters are: - Highly expensive.
- Consumer very less power.
- Cannot handle low-frequency signals.
The operation of the digital filter is determined by a program, which is stored in the memory of the processor. Hence, these filters are generally programmable. 30) The method responsible for introducing the aliasing effect in filters is: - Impulse invariant method.
- Bilinear transformation method.
- Both (a) and (b)
- None of the above
31) Which of the following is/are features of the digital signal processor? - It can handle real-time processing.
- It performs fast processing of arrays.
- On-chip registers of the processor cannot store intermediate results.
- Both (a) and (b).
32) Determine the discrete equation of the direct form-I structure shown in the below figure: - 3/4 y(n - 2) - 1/8 y(n - 3) + x(n) + 1/3x(n - 1)
- 3/4 y(n - 1) - 1/8 y(n - 2) + x(n) + 1/3x(n - 1)
- 3/4 y(n - 1) - 1/8 y(n - 2) + x(n) + 1/3x(n - 2)
- 3/4 y(n - 1) - 1/8 y(n - 3) + x(n) + 1/3x(n + 1)
The left side is the X(z). X(z) [1 + 1/3 z^-1] = W(z) X(Z) + 1/3 z^-1 X(z) = W(z) The inverse can be represented as: x(n) + 1/3x(n - 1) = w(n)
The right side is the Y(z). Y(z) = 3/4 z^-1 Y(z) - 1/8 z^-2 Y(z) + W(z) The inverse can be represented as: y(n) = 3/4 y(n - 1) - 1/8 y(n - 2) + w(n) Substituting the value of w(n) from step 1, we get: y(n) = 3/4 y(n - 1) - 1/8 y(n - 2) + x(n) + 1/3x(n - 1) It is the discrete equation of the given system. 33) Which of the following bus is used in the Digital signal processor? - Program memory bus
- Data memory bus
- Both (a) and (b)
- None of the above
34) Which of the following form is used for the IIR filters? - Direct form-I
- Indirect from-I
- Direct form-III
- Direct form IV.
35) The structure of the direct form- II is shown in the below figure. Determine the order of the system? - Second order system
- First order system
- Third order system
- None of the above
36) The multipliers required for the (M - 1) and (N - 1) order IIR filters are given by: - M + N + 1
- M + N - 2
- M + N - 1
- M + 2N + 1
M + N - 1 37) Find the number of block of the processed data with the input samples 16000 and the filter length 100. Assume the block size of FFT be 1024. - 17
- 35
- 34
- 15
N = 1024 M = 100 L = N - M + 1 = 1024 - 100 + 1 = 925 No. of blocks of the processed data = Input samples/ 925 = 16000/925 = 17.29 = 17 38) The incorrect statement about FIR filters is? - FIR filters are always stable.
- Its realization can be done using recursive structures.
- Its realization can be done using non-recursive structures.
- FIR filters are not immune to noise.
39) Which of the following feature about the triangular window technique used in the FIR filter design is correct? - The main lobe width is thrice that of rectangular window.
- The minimum stop band attenuation required for designing filters is 15 dB.
- The minimum stop band attenuation required for designing filters is 28 dB.
- Its side lobe magnitude of the window spectrum remains constant.
40) The incorrect statement about the effects of windowing in filters is: - The concept of windowing introduces side lobes.
- The windowing concept in the time domain results in the smoothing in the frequency domain.
- It helps in converting an infinite duration signal into finite.
- None of the above
41) The window technique whose main lobe width is 12pi/N is called: - Hamming window
- Blackmann window
- Kaiser window
- Rectangular window.
42) Which type of filters are all pole filters? - Type- I Chebyshev filters
- Type- II Chebyshev filters
- Both (a) and (b)
- None of the above
43) Which of the following statement is correct about Butterworth filters? 1. The magnitude response of the Butterworth filter has ripples in the pass-band. 2. Its pole lies on a circle in the s-plane. 3. Its design requires fewer parameters. 4. Its pole lies on an ellipse in the s-plane. - 1 and 3
- 2 and 3
- 1 and 4
- 1, 2, and 4
44) The incorrect statement about the Impulse Invariant method is: - No warping effect.
- It can easily convert discrete filters into analog filters.
- Absence of many-to-one mapping.
- It preserves the frequency characteristics.
45) The Nyquist sampling rate is given by: - Fs = 2 Fm
- Fs = 3 Fm
- Fs = 4 Fm
- Fs = Fm
46) Which of the following is/are standard test signals? - Step
- Impulse
- Exponential
- All of the above
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