The Dolph-Chebyshev Window (or Chebyshev window, or
Dolph window) minimizes the Chebyshev norm of the side
lobes for a given main-lobe width
[61,101],
[224, p. 94]:
![]() |
(4.43) |
An equivalent formulation is to minimize main-lobe width subject to a side-lobe specification:
![]() |
(4.44) |
The optimal Dolph-Chebyshev window transform can be written in closed form [61,101,105,156]:
The zero-phase Dolph-Chebyshev window,
, is then computed as the
inverse DFT of
.4.14 The
parameter controls the side-lobe level via the formula [156]
Side-Lobe Level in dB![]() |
(4.45) |
The Chebyshev window can be regarded as the impulse response of an optimal Chebyshev lowpass filter having a zero-width pass-band (i.e., the main lobe consists of two ``transition bands''--see Chapter 4 regarding FIR filter design more generally).