Update Content - 2022-03-15

content/zettels/decimation.md

@@ -108,6 +108,24 @@ Which is much more efficient that the single stage decimation.
 
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+There are two **practical issues** to consider for two-stage decimation:
+
+-   First, if the dual-filter system is required to have a pass-band peak-peak ripple of \\(R\\) dB, then both filters must be designed to have a pass-band peak-peak ripple of no greater than \\(R/2\\) dB.
+-   Second, the number of multiplications needed to compute each \\(x\_{\text{new}}(m)\\) output sample is much larger than \\(N\_\text{total}\\) because we must compute so many \\(\text{LPF}\_1\\) and \\(\text{LPF}\_2\\) output samples destined to be discarded.
+
+In order to cope with the second issue, an efficient decimation filter implementation scheme called _polyphase decomposition_ can be used.
+
+<summary>The advantages of two stage decimation, over single-stage decimation are:
+
+<ul class="org-ul">
+<li>an overall reduction in computation workload</li>
+<li>reduced signal and filter coefficient data storage</li>
+<li>simpler filter designs</li>
+<li>a decrease in the ill effects of finite binary-work-length filter coefficients</li>
+</ul>
+
+These advantages become more pronounced as the overall desired decimation factor \(M\) becomes larger.</summary>
+
 
 ## References: {#references}