### Example Chebyshev Windows and Transforms

Figure 3.31 shows the Dolph-Chebyshev window and its transform
as designed by `chebwin(31,40)` in Matlab, and
Fig.3.32 shows the same thing for `chebwin(31,200)`.
As can be seen from these examples, higher side-lobe levels are
associated with a narrower main lobe and more discontinuous endpoints.

Figure 3.33 shows the Dolph-Chebyshev window and its transform
as designed by `chebwin(101,40)` in Matlab. Note how the
endpoints have actually become *impulsive* for the longer window
length. The Hamming window, in contrast, is constrained to be
monotonic away from its center in the time domain.

The ``equal ripple'' property in the frequency domain perfectly
satisfies worst-case side-lobe specifications. However, it has the
potentially unfortunate consequence of introducing ``impulses'' at the
window endpoints. Such impulses can be the source of ``pre-echo'' or
``post-echo'' distortion which are time-domain effects not reflected
in a simple side-lobe level specification. This is a good lesson in
the importance of choosing the right *error criterion* to
minimize. In this case, to avoid impulse endpoints, we might add a
continuity or monotonicity constraint in the time domain (see
§3.13.2 for examples).

**Next Section:**

Chebyshev and Hamming Windows Compared

**Previous Section:**

Matlab for the Dolph-Chebyshev Window