Polyphase filtering is a powerful technique in [digital signal processing](https://www.ampheo.com/c/dsp-digital-signal-processors) ([DSP](https://www.ampheo.com/c/dsp-digital-signal-processors)) that improves the efficiency of multirate operations like decimation (downsampling) and interpolation (upsampling). It's especially useful when working with large sample rate changes or designing efficient filter banks.

**What Is Polyphase Filtering?**
At its core, polyphase filtering involves breaking a filter into multiple smaller sub-filters, called polyphase components, each responsible for a subset of the output. This allows for:

* Efficient implementation
* Reduced computation
* Better performance in real-time systems

**Use Cases**

**Key Concepts**
**1. Decimation (Downsampling)**
* Reduces the sampling rate by a factor M
* Naively: filter → keep every Mth sample
* Polyphase version: Split the filter into M sub-filters; compute only what's needed for each output sample

**2. Interpolation (Upsampling)**
* Increases the sampling rate by a factor L
* Naively: insert zeros → filter
* Polyphase version: Use L sub-filters, each computing part of the upsampled output without wasting effort on zero samples

**Mathematical View**
Let h[n] be your FIR filter and 𝑀 your decimation factor. The polyphase components are:
hk​[n]=h[nM+k],for k=0,1,...,M−1
The output is then computed using only the necessary phase components.

**Benefits**
* Computational Efficiency: Avoids unnecessary multiplies with zero (e.g., in upsampling)
* Lower Memory Footprint: Works with smaller sub-filters
* Pipeline-Friendly: Well-suited for hardware/[DSP](https://www.onzuu.com/category/dsp) chips

**Applications**
* Audio compression (e.g., MP3, AAC)
* Sample rate converters
* Digital communications (e.g., multicarrier systems)
* Software-defined radios

**Summary**