Half-band filter

Half-band filter

A half-band filter is a type of low-pass filter that has equal pass-band and stop-band ripples. The pass-band-edge and stop-band-edge frequencies are equidistant from the half-band frequency, which is either π/2 or f s /4, where f s is the sampling frequency. Additionally, half of the filter coefficients in a half-band filter are zero.From: Discrete Cosine Transform [2019], A Low-Complexity Multiplier-Less Filter Bank Based on Modified IFIR for the SDR Channelizer [2023]

Transform Mirroring and Rotation

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Published in Humberto Ochoa-Domínguez, K. R. Rao, Discrete Cosine Transform, 2019

Humberto Ochoa-Domínguez, K. R. Rao

The left-hand side of (8.46) is an odd function then l in the right-hand side must be an odd number. Therefore, we can multiply both sides of (8.46) by ejωl, incorporate these delays to the product filter and do P0(ω + π) = −P0(ω + π) then, P0(ω)+P0(ω+π)=2, which is the condition of the normalized product filter for perfect reconstruction. Notice that the product filter is a half band low pass filter. A half-band filter is a low-pass filter with same pass-band and stop-band ripples and the pass-band-edge and stop-band-edge frequencies are equidistant from the half-band frequency π/2 or fs/4, where fs is the sampling frequency. In other words, the frequency response of the filter is anti-symmetric around π/2 [455].

A Low-Complexity Multiplier-Less Filter Bank Based on Modified IFIR for the SDR Channelizer

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Journal Information

Published in IETE Journal of Research, 2023

Rinu C. Varghese, A. Amir

By counting all the multipliers in the filter structure, the complexity of the filter structure is evaluated. The complexity of block 1 or modified low-complexity IFIR filter block is the required multiplier of the prototype base filter, which is the filter coefficient. To further reduce the complexity of the proposed structure, the base filter is designed as a half-band filter. In a half-band filter, half of the filter coefficients are zero [15].

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Transform Mirroring and Rotation

A Low-Complexity Multiplier-Less Filter Bank Based on Modified IFIR for the SDR Channelizer