Digital Signal Processing Reference
In-Depth Information
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(a) Frequency (DFT Bin)
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(b) Frequency (DFT Bin)
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(c) Frequency (DFT Bin)
Figure 3.40:
(a) Comparison of DFT response to a signal having closely-spaced on-bin frequencies
with added noise for various windows-Boxcar: solid; Kaiser(5): dotted; Blackman: dash-dot; Hamming:
dashed; (b) Comparison of DFT response to closely-spaced off-bin frequencies with added noise for
various windows, plotted as in (a); (c) Comparison of DFT response to widely spaced, off-bin discrete
frequencies with added noise, plotted as in (a). In each case the discrete test frequencies are marked with
vertical lines.
discrimination. Each frequency, in this case, will either correlate perfectly with a DFT correlator, or
not at all. Hence, the problem of leakage will exist in this case only with respect to wideband noise
components in the signal which, if present, will contaminate all bins, lowering the signal-to-noise
ratio and blurring the distinction among bins close to each other.
3.17.6 ADDITIONAL WINDOW USE
Windows are also commonly applied to FIR impulse responses. A later chapter (found in Volume III of
the series) on basic FIR design will explore the benefits and tradeoffs associated with different windows
used in FIR design.
3.18
DTF T VIA PADDED DF T
The DFT evaluates the frequency response of a sequence of length
N
at roughly
N/
2 frequencies such
as 0, 1, etc. The DTFT can be evaluated at any number of arbitrary frequencies (such as 1.34, 2.66,3,
etc.), and thus can provide a far better estimate of the true frequency response of a sequence or system,
provided a large enough number of samples are computed. By padding a sequence with zeros to a quite
extended length, correlations of the sequence with many more discrete frequencies are performed, leading
to a much more detailed spectrum. This is particularly useful when the padded sequence is long since, as
