1.Decimation-in frequency FFT algorithm is used to compute H(k).
a) True
b) False
Explanation:The N-point DFT of h(n), which is padded by L-1 zeros, is denoted as H(k). This computation is performed once via the FFT and resulting N complex numbers are stored. To be specific we assume that the decimation-in frequency FFT algorithm is used to compute H(k). This yields H(k) in the bit-reversed order, which is the way it is stored in the memory
2. How many complex multiplications are need to be performed for each FFT algorithm?
a) (N/2)logN
b) Nlog2N
c) (N/2)log2N
d) None of the mentioned
Explanation: The decimation of the data sequence should be repeated again and again until the resulting sequences are reduced to one point sequences. For N=2v, this decimation can be performed v=log2N times. Thus the total number of complex multiplications is reduced to (N/2)log2N
3. How many complex additions are required to be performed in linear filtering of a sequence using FFT algorithm?
a) (N/2)logN
b) 2Nlog2N
c) (N/2)log2N
d) Nlog2N
Explanation: The number of additions to be performed in FFT are Nlog2N. But in linear filtering of a sequence, we calculate DFT which requires Nlog2N complex additions and IDFT requires Nlog2N complex additions. So, the total number of complex additions to be performed in linear filtering of a sequence using FFT algorithm is 2Nlog2N.
4. How many complex multiplication are required per output data point?
a) [(N/2)logN]/L
b) [Nlog22N]/L
c) [(N/2)log2N]/L
d) None of the mentioned
Explanation: 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 FFT algorithm are (N/2)log2N. So, the number of complex multiplications per output data point is [Nlog22N]/L.
5.The effect of round off errors due to the multiplications performed in the DFT with fixed point arithmetic is known as Quantization error.
a) True
b) False
Explanation: Since DFT plays a very important role in many applications of DSP, it is very important for us to know the effect of quantization errors in its computation. In particular, we shall consider the effect of round off errors due to the multiplications performed in the DFT with fixed point arithmetic
6. What is the model that has been adopt for characterizing round of errors in multiplication?
a) Multiplicative white noise model
b) Subtractive white noise model
c) Additive white noise model
d) None of the mentioned
Explanation: Additive white noise model is the model that we use in the statistical analysis of round off errors in IIR and FIR filters
7. How many quantization errors are present in one complex valued multiplication?
a) One
b) Two
c) Three
d) Four
Explanation: We assume that the real and imaginary components of {x(n)} and {WNkn} are represented by ‘b’ bits. Consequently, the computation of product x(n). WNkn requires four real multiplications. Each real multiplication is rounded from 2b bits to b bits and hence there are four quantization errors for each complex valued multiplication
8. What is the total number of quantization errors in the computation of single point DFT of a sequence of length N?
a) 2N
b) 4N
c) 8N
d) 12N
Explanation: Since the computation of single point DFT of a sequence of length N involves N number of complex multiplications, it contains 4N number of quantization errors.
9. What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?
a) (0,Δ)
b) (-Δ,0)
c) (-Δ/2,Δ/2)
d) None of the mentioned
Explanation: The Quantization errors due to rounding off are uniformly distributed random variables in the range (-Δ/2,Δ/2) if Δ=2-b. This is one of the assumption that is made about the statistical properties of the quantization error.
10. The 4N quantization errors are mutually uncorrelated.
a) True
b) False
Explanation: The 4N quantization errors are mutually uncorrelated. This is one of the assumption that is made about the statistical properties of the quantization error.