WorksheetsDiscrete Fourier Transform Quiz
Total questions: 25
Worksheet time: 13mins
What is the main purpose of the Discrete Fourier Transform (DFT)?
Compress data
Filter noise
Convert time-domain data to frequency-domain
Encrypt signals
DFT is applied to:
Continuous signals
Discrete signals
Random signals
Periodic analog signals
For a decimation-in-time FFT algorithm, which of the following is true?
Both input and output are in order
Both input and output are shuffled
Input is shuffled and output is in order
Input is in order and output is shuffled
The DFT is defined over:
Finite duration sequences
Infinite sequences
Random signals
Continuous signals
Which of the following is a property of DFT?
Linearity
Time-shifting
Convolution
All of the above
The DFT is equivalent to evaluating the DTFT at:
Evenly spaced frequencies
All possible frequencies
Zero frequency
Random frequencies
The number of complex multiplications required for an N-point DFT is:
N
N log N
N²
log N
The DFT is periodic with period:
N
N/2
2N
1/N
What is FFT?
An approximation to DFT
A type of filter
An efficient algorithm to compute DFT
None of the above
The FFT reduces computational complexity from O(N²) to:
O(N log N)
O(N)
O(log N)
O(1)
Which of the following FFT algorithms is most commonly used?
Radix-2
Radix-3
Radix-4
Radix-6
In radix-2 FFT, the number of stages for N-point sequence is:
N
log₂N
√N
N²
Which operation is most reduced in FFT compared to DFT?
Additions
Subtractions
Multiplications
All of the above
The term "butterfly" in FFT refers to:
A type of signal
A graphical representation of filter response
A computation structure
A phase angle
In FFT, the twiddle factor is defined as:
e^(j2π/N)
e^(−j2π/N)
e^(−jπ/N)
e^(jπ/N)
Which technique is used in FFT to reduce complexity?
Zero padding
Convolution
Decimation
Oversampling
Which of the following is true about FFT and DFT?
FFT and DFT give different results
FFT is a faster way to compute DFT
FFT approximates DFT
FFT is less accurate than DFT
In practical implementations, FFT is commonly used in:
Weather forecasting
Image compression
Audio signal processing
All of the above
How many complex additions are required to be performed in linear filtering of a sequence using FFT algorithm?
(N/2)logN
2Nlog2N
(N/2)log2N
Nlog2N
What is the DFT of the four point sequence x(n)={0,1,2,3}
{6,-2+2j-2,-2-2j}
{6,-2-2j,2,-2+2j}
{6,-2+2j,-2,-2-2j}
{6,-2-2j,-2,-2+2j}
What is the circular convolution of the sequences X 1 (n)={2,1,2,1} and X 2 (n)={1,2,3,4}?
{16,16,14,14}
{14,16,14,16}
{14,14,16,16}
None of the mentioned
What is the linear convolution of the sequences X 1 (n)={2,1,2,1} and X 2 (n)={1,2,3,4}?
y(n)={2, 5, 10, 16, 12, 11, 4}
y(n)={2, 10, 5, 16, 12, 11, 4}
y(n)={2, 5, 10, 16, 18, 11, 4}
y(n)={2, 5, 10, 16, 12, 18, 4}
In FFT, if x(n) is real, then as per complex conjugate property:
X(k)=−X(k)
X(k)=X(N−k)*
X(k)=X(N−k)X(k)
X(k)=−X(N−k)*X(k)
What is the circular convolution of the sequences X 1 (n)={2,2,2,2} and X 2 (n)={1,2,3,4}?
{21,20,14,14}
{20,21,14,16}
{20,20,20,20}
None of the mentioned
What is the linear convolution of the sequences X 1 (n)={1,2,3,4} and X 2 (n)={1,2,3,4}?
y(n)={1,4,10,20,25,24,16}
y(n)={1,4,10,25,25,24,16}
y(n)={1,4,10,20,35,24,16}
y(n)={1,4,10,20,45,24,16}
