Digital Filtering Using the FFT - Practical Analog and Digital Filter Design - page 213

Figure 9.3 DFT of three frequency lengths with Hamming window.

It can be shown that the frequency resolution ∆ f of the DFT is improved by
increasing the number of time domain samples, as shown in (9.5). As N increases,
the ability to see smaller frequency details improves regardless of window type
used. The coefficient m w is a windowing factor that takes on a value of 1 for a
rectangular window, approximately 2 for a Hamming window, and other values
for Kaiser based on the β value chosen. (See Orfanidis' text for further details.)

f

1

s

∆ f = m ⋅ = m ⋅

(9.5)

w w

N T ⋅ N

s

Example 9.3 Determine Resolution for DFT System

Problem: Determine the number of time domain samples needed to resolve
the three frequencies of Examples 9.1 and 9.2.