Digital Signal Processing Quiz

Which of the following is true about the Discrete Fourier Series (DFS)?

• DFS is used for non-periodic sequences only.

• DFS is the representation of a periodic sequence in the frequency domain.

• DFS does not involve complex exponentials.

• DFS is only applicable to continuous-time signals.

What is the primary difference between DFT and DFS?

• DFT is for continuous-time sequences; DFS is for discrete-time sequences.

• DFT applies to finite-length sequences; DFS applies to periodic sequences.

• DFS is only for real-valued sequences, while DFT is for complex sequences.

• There is no difference; they are the same.

Which method ensures efficient computation of linear convolution using DFT for long sequences?

• Zero-padding

• Overlap-Add method

• Overlap-Save method

• Both B and C

Which of the following is a property of the DFT?

• Time shifting results in a frequency-domain shift.

• Time shifting results in a time-domain shift.

• The DFT is invariant under time shifting.

• The DFT results in a time-domain shift but not a frequency-domain shift.

Parseval's Theorem in the context of DFT states that:

• The sum of the absolute values of the sequence is equal to the sum of the absolute values of the DFT.

• The energy in the time domain is equal to the energy in the frequency domain.

• The time-domain energy is doubled when transformed to the frequency domain.

• The energy in the time domain is half the energy in the frequency domain.

Which method is used to compute the linear convolution of two sequences using DFT?

• Zero-padding method

• Overlap-Add method

• Half-overlap method

• Circular Convolution method

In the Overlap-Save method, the sequences are:

• Split into non-overlapping segments

• Shifted by one sample at a time

• Split into overlapping segments and discarded after processing

• Not split at all

The DFT can be computed efficiently using:

• Discrete-Time Fourier Transform (DTFT)

• Fast Fourier Transform (FFT)

• Z-Transform

• Laplace Transform

What is the main difference between the Radix-2 Decimation-in-Time (DIT) and Radix-2 Decimation-in-Frequency (DIF) FFT algorithms?

• DIT splits the sequence into even and odd parts, while DIF divides it based on frequency components.

• DIT computes the FFT in time domain, while DIF computes it in frequency domain.

• DIT and DIF are two names for the same algorithm with no structural difference.

• DIT operates on sequences of length 2n2^n2n, while DIF works for arbitrary sequence lengths.

Which of the following describes the Radix-2 Decimation-in-Time (DIT) FFT algorithm?

• The sequence is recursively split into even and odd indexed parts.

• The sequence is divided into frequency components recursively.

• The sequence is split into blocks of size 2.

• None of the above