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]:
An equivalent formulation is to minimize main-lobe width subject to a side-lobe specification:
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 
|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).