Application of linear optimization technique to design a fixed coefficient multiplierless sample rate conversion filter for multiple-of-three decimation factor

Multirate sampling is used to increase or decrease the original sampling rate of signal. Decimation decreases the original sampling rate while interpolation increases it. Simplest of decimation filter is comb filter. In this paper a Cascaded Integrator Comb sample rate conversion filter for multiple-of - three decimation factor is designed. The linear programming optimization technique is used to flatten passband of filter and expanded cosine filter is used to increase the stopband attenuation in third folding band. The results indicate that the proposed filter shows less passband droop with increase in stopband attenuation. The proposed design has passband droop
$\leq 0.009\ \text{dB}$
with alias rejection
$\leq-156\text{dB}$
in first folding band. The passband droop has improved by 99% approximately.