In digital signal processing or DSP digital filters are as important as engines in vehicles. Among the several types of Digital Filters available FIR and IIR has the lion’s share.

The fundamental algorithms used by digital signal processors are digital filters, both types of digital filters are used in practice. Let’s break each down to our understanding.

## What Is the Basic of a Digital Filter?

The fundamental idea behind a digital filter is the use of mathematical methods to change or extract particular elements from a discrete-time signal. It works by generating output samples by applying a set of coefficients to input samples. The filter’s behavior and filtering properties are established by these coefficients.

**Figure 1:** **Block Diagram of a Digital Filter**

**Finite impulse response (FIR)** and **infinite impulse response (IIR)** are two categories for digital filters. Due to its reliance only on a limited number of input samples and filter coefficients, FIR filters have a finite impulse response. IIR filters, in contrast, have an infinite impulse response and base their output on both past and present input samples as well as previous output samples.

## Two Types of Digital Filter

The two fundamental classes of digital filters namely **FIR **and **IIR **are discussed briefly in the following.

### Finite Impulse Response (FIR) Filters

**FIR filters** have a finite impulse response, meaning their output is solely dependent on a finite number of input samples and filter coefficients. The key factor of such kind of digital filters is henceforth the requirement of finite memory.

Since both inputs and memory are finite, the stability of FIR is greatly enhanced. Moreover, the phase response is linear. Audio equalizers often use FIR and they are perfect for that because in those cases phase distortion is targeted to be receded. This can be easily achieved through simple convolution techniques.

### Infinite Impulse Response (IIR) Filters

**IIR filters** have an infinite impulse response, considering both past and present input and output samples to determine their output. But the values gradually reduce.

What makes IIR exclusive from its counterpart is the feedback path. This comes in a lot of handy in innumerable circumstances but due to its recursivity situation may jeopardize bringing in instability. Most practical RTS systems utilize IIR.

## What Is the Difference Between Digital Filters

An aspect-by-aspect differentiation between FIR and IIR is drawn below.

### Impulse Response

**FIR Filter:** The impulse response of an FIR filter is finite in length, meaning it only considers a finite number of input samples and coefficients to compute the output.

**IIR Filter:** The impulse response of an IIR filter is infinite in length, taking into account both past and present input samples as well as past output samples.

### Stability

**FIR Filter:** FIR filters are inherently stable as they do not rely on feedback loops, making them more suitable for applications that require strict stability guarantees.

**IIR Filter:** IIR filters can exhibit stability issues due to feedback loops, requiring careful design and analysis to ensure stability.

### Frequency Response

**FIR Filter:** FIR filters can achieve a linear phase response, meaning they preserve the relative phase relationships between different frequency components of the input signal.

**IIR Filter:** IIR filters may introduce phase distortion due to their recursive nature, resulting in non-linear phase responses.

### Implementation Complexity

**FIR Filter:** FIR filters can be implemented using simple and efficient algorithms, such as the convolution operation, without the need for feedback loops.

**IIR Filter:** IIR filters generally require more complex implementation techniques, such as recursive algorithms or difference equations, due to their feedback structure.

### Filtering Characteristics

**FIR Filter:** FIR filters are typically better suited for applications requiring precise control over the filter’s frequency response, as they can provide sharp cutoffs and low passband ripple.

**IIR Filter:** IIR filters are often used when a more efficient implementation or a specific frequency response shape, such as a peak or notch filter, is desired.

## Frequently Asked Questions and Answers

### Why Are Digital Filters Used?

Digital filters are used to modify signal frequency content, enhance or suppress specific components, remove noise or interference, and achieve desired signal processing goals. They are widely applied in audio and video processing, telecommunications, image processing, control systems, and more.

### What Are the Most Common Digital Filters?

Although UV is still the most commonly used filter today, its function has changed. It primarily protects a lens from scuffing and damage. UV filters should be used by all photographers who are concerned about their equipment.

## Conclusion

In summary, digital filters can be broadly categorized into two types: FIR filters and IIR filters. Understanding these types is crucial for effective filter application in signal processing across various fields, including audio, video, image processing, control systems, and more.

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