Chap5 IEEE 802 pdf

Associate Professor

Dept. of Electrical and Electronic Engineering

University of Dhaka

Dr. Mohammad Junaebur Rashid (JR)

ICT3105

:

Digital Signal Processing

(3.0 Cr)

Course Teacher

Bangladesh University of Professionals

Lecture 23

Design of FIR Filter

• "FIR" means "Finite Impulse Response".

• _{Why is the impulse response "finite" ?}

- Because there is no feedback in the FIR.

- _{A lack of feedback guarantees that the impulse response will be finite.}

Advantages of FIR (compared to IIR) Filters

• Easily be designed to be "linear phase"

– _{Put simply, linear-phase filters delay the input signal but don’t distort its phase.} • _{Simple to implement.}

– _{On most DSP microprocessors, the FIR calculation can be done by looping a single}

instruction.

Lecture 23

Design of FIR Filter

h(k), k = 0, 1, … , N - 1 are the Impulse Response (coefficients), H(z) is the Transfer Function,

N is the Filter Length (No. of Filter Coefficients) of the filter.

FIR equations

Difference Equation

System function (Transfer function) equation

Linear Phase Response

• "Linear Phase" refers to the condition where the phase response of the filter is a linear

(straight-line) function of frequency (excluding phase wraps at +/- 180 degrees).

• This results in the delay through the filter being the same at all frequencies.

• _{Therefore, the filter does not cause "phase distortion" or "delay distortion".}

• _{The lack of phase/delay distortion is an advantage of FIR filters over IIR and analogue}

Lecture 23

Design of FIR Filter

Phase Delay and Group delay

• The Phase Delay (Tp) or Group Delay (Tg) of the filter is a measure of how a filter

modifies the phase characteristics of the signal.

• _{Consider a signal consisting of several frequency components, like: Speech}

waveform, or a Modulated signal

• _{Phase Delay (Tp) =}

is the amount of time delay of each frequency component of the signal suffers in

going through the filter.

• _{Group Delay (Tg) = is the average time delay of all}

Lecture 23

Design of FIR Filter

Problem of non-linear phase filter

• A non-linear phase filter will cause phase distortion in the signal that passes through it.

• This is due to the fact that the frequency components in the signal will each be delayed

by an amount NOT proportional to frequency, hence altering their harmonic

relationship.

• _{This distortion is extremely undesirable in applications involving: Music, Data}

transmission, Video, and Bio-medical applications

• _{This distortion can be avoided by using filters with linear phase characteristics.}

• _{Non-linear phase filters will distort the audio of AM broadcast signals, blur the edges of}

television video images, blunt the sharp edges of received radar pulses, and increase

data errors in digital communication signals.

• None-linear phase filters are also called “minimum phase (*)” * least amount of group

Lecture 23

Design of FIR Filter

Types of linear phase FIR filters

4 types of linear phase FIR filters

• Type 1 –most versatile

• Type 2 – frequency response is always 0 at ω=π. (not suitable as a high-pass filter)

• Type 3 and 4 – Introduce a π/2 phase shift, frequency response is always 0 at ω=π.

Lecture 23

Design of FIR Filter

Type 1 and 2 FIR coefficients

• Type-1: Positive symmetry, Odd length of Coefficients

• Example impulse response -

• Type-2: Positive symmetry, Even length of Coefficients

Lecture 23

Design of FIR Filter

Type 3 and 4 FIR coefficients

Type 3 [Negative Symmetry, Odd Length (Coefficients)]: 90° phase shift

Always zero at f = 0, hence unsuitable as a Low-pass filter.

In addition, always zero at f = 0.5, hence unsuitable as a High-pass filter.

The sample impulse response is given by:

Lecture 23

Design of FIR Filter

Steps for designing FIR filter

5 Steps:

1. Determine the filter specifications

2. Choose a suitable filter structure

3. Calculate the filter coefficient values

4. Analysis the finite wordlength effect

Lecture 23

Design of FIR Filter

Lecture 23

Design of FIR Filter

Tolerance scheme with normalized filter parameters

• passband= 0.18 – 0.33

• transition band= 0.14 – 0.18

and 0.33 – 0.37

• _{stopband= 0 – 0.14 and 0.37}

– 0.5

• stopband deviation, δ_s= 0.001

• passband deviation, δ_p= 1.05,

1, 0.95

• 1 + δ_p= 1.05

Lecture 23

Design of FIR Filter

Normalized filter parameters

•

passband= 0.18 – 0.33

•

transition band= 0.14 – 0.18 and

0.33 – 0.37

•

stopband= 0 – 0.14 and 0.37 –

0.5

•

stopband deviation, δ

= 0.001

•

passband deviation, δ

= 1.05, 1,

0.95

•

1 + δ

= 1.05

•

1 – δ

= 0.95

Un-normalized filter parameters

With sampling frequency of 10 kHz:

•

Passband=1.8 - 3.3 kHz

•

Stopband(s)=0 - 1.4 kHz and 3.7 -

5 kHz

•

Stopband Attenuation

(A

)=-20 log

δ

=-20 log

(0.001)

=60 dB

•

Passband Ripple (A

)=20 log

δ

=20 log

(1 + 0.05)

Lecture 23

Design of FIR Filter

Window Method:

• _{Offers a very simple and flexible way of computing FIR filter coefficients.}

• _{However, does not allow the over the filter parameters. designer adequate control}

The Optimal Method

• _{With efficient and easy-to-use programs it is now widely used in industry.}

• _{For most applications, this method will yield the desired FIR filter.}

• _{Should be the first choice, unless a particular application dictates otherwise, or a CAD}

facility is unavailable.

The Frequency Sampling Method

• _{The main attraction is that it allows for a recursive realization of FIR filters, which can}

be computationally very efficient.

Lecture 23

Design of FIR Filter

Steps of Window method

Step 1: Specify the “ideal” or desired frequency response of the filter, H_D(ω).

Step 2: Obtain the IDEAL impulse response, h_D(n), of the desired filter by evaluating the

IDFT.

Step 3: Select a window function w(n) that satisfies the passband and stopband

attenuation specifications. Determine the filter length N.

Step 4: Multiply the ideal coefficients by the selected window function to get the filter

Lecture 23

Design of FIR Filter

Ideal Impulse response for LP Filter

Ideal frequency response for LP

Ideal (infinite)Impulse response for LP

• Note that h_D(n) is symmetrical about n = 0 (i.e. h_D(n) = h_D(-n)), so the filter will have linear

phase response.

• Although h_D(n) decreases as we move away from n = 0, the impulse response is infinite in

length (as n = ±∞).

Lecture 23

Design of FIR Filter