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Solved Examples - Discrete Fourier Transform | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download
Example 1
Verify Parseval’s theorem of the sequence 
Solution − 
We can see that, LHS = RHS.(Hence Proved)
Example 2
Compute the N-point DFT of x(n) = 3δ(n)
Solution − We know that,
So, 
Example 3
Compute the N-point DFT of x(n) = 7(n−n0)
Solution − We know that,
Substituting the value of x(n),
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FAQs on Solved Examples - Discrete Fourier Transform - Digital Signal Processing - Electronics and Communication Engineering (ECE)
| 1. What is the Discrete Fourier Transform (DFT)? |  |
Ans. The Discrete Fourier Transform (DFT) is a mathematical transformation that converts a discrete sequence of time-domain samples into a sequence of complex frequency-domain samples. It is commonly used in signal processing to analyze the frequency components of a signal.
| 2. How is the Discrete Fourier Transform different from the Fast Fourier Transform (FFT)? | |
Ans. The Discrete Fourier Transform (DFT) is a general mathematical algorithm that computes the frequency-domain representation of a signal, while the Fast Fourier Transform (FFT) is a specific algorithm that efficiently computes the DFT. The FFT is a faster implementation of the DFT, making it more commonly used in practice.
| 3. What are the applications of the Discrete Fourier Transform? | |
Ans. The Discrete Fourier Transform (DFT) has various applications in fields such as audio processing, image processing, telecommunications, radar signal analysis, and medical imaging. It is used for tasks such as spectral analysis, filtering, compression, and pattern recognition.
| 4. How can I calculate the Discrete Fourier Transform of a sequence? | |
Ans. To calculate the Discrete Fourier Transform (DFT) of a sequence, you can use the formula that expresses the DFT as a linear combination of complex exponentials. Alternatively, you can use software libraries or programming languages that provide built-in functions for computing the DFT, such as the numpy.fft module in Python.
| 5. Can the Discrete Fourier Transform be used for real-time signal processing? | |
Ans. Yes, the Discrete Fourier Transform (DFT) can be used for real-time signal processing. However, the computational complexity of the DFT is relatively high, especially for large sequences. In such cases, the Fast Fourier Transform (FFT) algorithm is often preferred for its faster computation time. Additionally, there are optimized FFT implementations specifically designed for real-time processing.
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