**Directions: **Read the passage and answer the following four questions.

A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be general-purpose such as a PC or specialized DSP chip. The analog input signal must first be sampled and digitized using an ADC. The resulting binary numbers, representing successive sampled values of the signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. The results of these calculations, which now represent sampled values of the filtered signal, are converted back to the single using a DAC

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UGC NET Paper 2 (Electronic Science): December 2018 Official Paper

Option 3 : Non-recursive FIR filter

Official Paper 1: Held on 24 Sep 2020 Shift 1

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__Explanation:__

**Recursive filter**

*Recursive filters*, also known as *Infinite Impulse Response* (IIR) filters, are filters where the output sample is a linear combination of some number of previous inputs and outputs.

**Non Recursive filter**

A non-recursive filter only uses input values like x[n − 1], unlike a recursive filter where it uses previous output values like y[n − 1].

In signal processing, non-recursive digital filters are often known as Finite Impulse Response (FIR) filters, as a non-recursive digital filter has a finite number of coefficients in the impulse response h[n].

Examples:

- Non-recursive filter: y[n] = 0.5x[n − 1] + 0.5x[n]
- Recursive filter: y[n] = 0.25y[n − 1] + 1.5x[n]

Given filter response is \(h\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} { - 2;}&{n = 2,4}\\ {2;}&{n = 1,3}\\ {0;}&{otherwise} \end{array}} \right.\)

Graphical representation of the filter is:

The samples are existing at n = 1, 2, 3, 4 only.

The output expression is:

Y[n] = 2h[n -1] – 2h[n -2] +2h[n -3] -2h[n -4]

__Conclusion:__

There is no previous output sample so it is a non-recursive filter.