31. How many complex multiplications is required per output data point?
A. [(N/2)logN]/L
B. [Nlog22N]/L
C. [(N/2)log2N]/L
D. None of the mentioned
Answer: B
In the overlap-add method, the N-point data block consists of L new data points and additional M-1 zeros and the number of complex multiplications required in the FFT algorithm are (N/2)log2N. So, the number of complex multiplications per output data point is [Nlog22N]/L.
31. If the desired number of values of the DFT is less than log2N, a direct computation of the desired values is more efficient than the FFT algorithm.
A. True
B. False
Answer: A
To calculate an N point DFT using the FFT algorithm, we need to perform (N/2) log2N multiplications and N log2N additions.
But in some cases where the desired number of values of the DFT is less than log2N such a huge complexity is not required.
So, direct computation of the desired values is more efficient than the FFT algorithm.
32. What is the transform that is suitable for evaluating the z-transform of a set of data on a variety of contours in the z-plane?
A. Goertzel Algorithm
B. Fast Fourier transform
C. Chirp-z transform
D. None of the mentioned
Answer: C
The chirp-z transform algorithm is suitable for evaluating the z-transform of a set of data on a variety of contours in the z-plane.
This algorithm is also formulated as linear filtering of a set of input data. As a consequence, the FFT algorithm can be used to compute the Chirp-z transform.
33. According to Goertzel Algorithm, if the computation of DFT is expressed as a linear filtering operation, then which of the following is true?
A. yk(n)=\(\sum_{m=0}^N x(m)W_N^{-k(n-m)}\)
B. yk(n)=\(\sum_{m=0}^{N+1} x(m)W_N^{-k(n-m)}\)
C. yk(n)=\(\sum_{m=0}^{N-1} x(m)W_N^{-k(n+m)}\)
D. yk(n)=\(\sum_{m=0}^{N-1} x(m)W_N^{-k(n-m)}\)
Answer: D
Since WN-kN = 1, multiply the DFT by this factor. Thus
38. If the contour is a circle of radius r and the zk are N equally spaced points, then what is the value of zk?
A. re-j2πkn/N
B. rejπkn/N
C. rej2πkn
D. rej2πkn/N
Answer: D
We know that, if the contour is a circle of radius r and the zk are N equally spaced points, then what is the value of zk is given by rej2πkn/N
39. How many multiplications are required to calculate X(k) by chirp-z transform if x(n) is of length N?
A. N-1
B. N
C. N+1
D. None of the mentioned
Answer: C
We know that yk(n)=WN-kyk(n-1)+x(n).Each iteration requires one multiplication and two additions. Consequently, for a real input sequence x(n), this algorithm requires N+1 real multiplications to yield not only X(k) but also, due to symmetry, the value of X(N-k).
40. If the contour on which the z-transform is evaluated is as shown below, then which of the given condition is true?
A. R0>1
B. R0<1
C. R0=1
D. None of the mentioned
Answer: A
From the definition of chirp z-transform, we know that V=R0ejθ.
If R0>1, then the contour which is used to calculate z-transform is as shown below.