Chapter 03 The Discrete Fourier Transform

3.1

Let’s assume that we have performed a 20-point DFT on a sequence of real-valued time-domain samples, and we want to send our $X(m)$ DFT results to a colleague using e-mail. What is the absolute minimum number of (complex) frequency-domain sample values we will need to type in our e-mail so that our colleague has complete information regarding our DFT results?

Solution:

Since it is symmetric, we will just need send 10.

$\square$

3.2

Assume a systems engineer directs you to start designing a system that performs spectrum analysis using DFTs. The systems engineer states that the spectrum analysis system’s input data sample rate, $f_s$, is $1000$ Hz and specifies that the DFT’s frequency-domain sample spacing must be exactly $45$ Hz.

(a) What is the number of necessary input time samples, $N$, for a single DFT operation?

Solution: