Apply Discrete Fourier Transform (DFT) to the sequence (x) given below: x ={1 2 8 9}.

Verify whether the original sequence can be determined without any loss of information after Inverse Fourier Transform.

Applying Discrete Fourier Transform (DFT) to Sequence x = {1, 2, 8, 9}

Discrete Fourier Transform (DFT) is a mathematical technique used in signal processing and image analysis to transform a signal or sequence from its time or spatial domain to its frequency domain. In the context of this question, we are given a sequence \(x = \{1, 2, 8, 9\}\) and asked to apply the DFT to this sequence.

The Discrete Fourier Transform of a sequence \(x\) of length \(N\) is given by the formula:

\[ X(k) = \sum_{n=0}^{N-1} x(n) \cdot e^{-j2\pi nk/N} \]

Where:
- \( X(k) \) is _______ __________ ___ ___ ____.
__________ _________ _______ _________ _________ ____ _________ ____ ______ _______ _________ _____.
_____ __________ ____ _____ _________ ____ ________ ____ __________ ___ _____ ______.
_________ ______ _________ _______ _____ ____.
____ _______ ________ _____ _________.
_______ _________ _____ __________ ________.
______ ___ _________ ______ __________ ____ _______ ____ _______ _____.
________ ________ ______ _____ _____.
_______ _____ __________ ____ _______ _______ _____ ____.
_______ ____ _______ _____ ________ __________ ________ _______ _________ ________ _____ ___.
_________ ______ ___ ______ ______ __________.
_________ _________ _______ ______ _____ ____ _____ ________.
__________ _________ _______ ______ ___ _______ ______ ____ _________ _______ ___.
_______ ___ __________ ______ _________ __________ ____ ___ _________ ________ _____ ___.
_______ _________ _______ ___ _________ ______ _____ _______ ___.
_________ _____ __________ _____ _________ _______.
___ ________ ________ __________ _________ ______ ___ _________.
_____ _____ ____ ______ __________ _______ ________ ___ ________ ___.
_____ _______ _____ _________ __________ ______ ___ ____.
_______ _______ ______ _____ ____ __________ ____ __________ ____ _____ ____ _______.
__________ _________ ______ _________ ________ _______ ________ ________ _____ ____ ______.
_________ _____ __________ ______ _____ _______ _______ ___ ____.
______ ________ __________ _______ ___ _________.
______ _____ ___ _______ ____ ___ ________ _______.
____ ____ ____ _______ ____ ______ ______ ___ ________ ________ ________.
_________ _________ _______ ____ ___.
_____ _____ ____ _____ ________ __________ _________ _______ ________.
_______ ______ _________ ___ ___ __________ ______ ______ ____ _____ ____ __________.
____ ______ ________ _______ ________ __________ _______ ________.
_______ ___ _________ _______ _________ __________ _______ ________ _______.
_________ _____ __________ ___ ____ __________ ____ _______ _____ _______ _________ ______.
_________ ___ ____ ___ ______ _____ ____ _________ __________.
_________ ______ ___ _______ _________ _______ __________ ______ ___ ______ _______.
_________ ____ _______ ________ ______ ________ __________ ______ ________ ______.
__________ ___ __________ ____ ______ ________ ___.
Get Full Answer on WhatsApp