Finite Impulse Response (FIR) Filters

Filtering concept in time domainFiltering concept in time domain

Transformation ConsiderationsTransformation Considerations

Filter typesFilter types

• FIRFIR– Use only current and past input samplesAlso known as non recursive filters– Also known as non‐recursive filters

• IIR– In addition to current and past input samples, also use past output samples

FIR Example‐Averaging FilterFIR Example Averaging Filter

Averaging Filter structureAveraging Filter structure

Basic digital blocksBasic digital blocks

• AdderAdder• MultiplierShif i• Shift register

Generalized Block DiagramGeneralized Block Diagram

Averaging filter coefficients, frequency/phase (64 DFT)response (64‐pt DFT)

Averaging filter frequency responseAveraging filter frequency response

Sine wave input to filter with f = fs/32, f /3fs/32

Changing filter coefficientsChanging filter coefficients

5‐tap low pass filter block diagram5 tap low pass filter block diagram

Low pass filter design‐window methodLow pass filter design window method

Inverse DFT of H(m)Inverse DFT of H(m)

Effect of truncationEffect of truncation

Windows in FIR filter design

• Window function:• Window function: –To minimize the stop band ripples

Windows in FIR filter designg

Applying windowApplying window

Windows frequency response

LPF Filter’s frequency response d h d ff dmagnitude with different windows