Filter Design - Non Recursive

Question 1

Whats the general form of the casual LTI processor:

Answer 1

Question 2

What are the idealised responses for low pass, high pass, bandpass and band stop

Answer 2

Question 3

What is the frequency response and transfer function that corresponds to the difference equation relating to the output of a non recurisive filter.

Answer 3

Question 4

What are non recursive filters equal to - what are the parts to this?

Answer 4

FIR Filter impulse response - Transfer function and frequency response are what this is made up of?

Question 5

What is H(Ω) to?

Answer 5

The real function of Ω, implying a zero phase filter

Question 6

DEscribe what a simple moving average filter is? what is the supporting formula that goes along with this filter

Answer 6

Question 7

Describe how the frequency response magnitude characteristics configurations can be show… and how 21 terms and 51 terms may change the result respectively

Answer 7

Question 8

How might a simple bandpass filter be derived from a low pass prototyple? - graphic

Answer 8

Question 9

Summarize how a high or band pass filter may be deived from a low pass filter

Answer 9

multiply (modulate) the origional impulse response by signal cos(nΩ0) where Ω0 = desired center frequency of the new filter

(knowing that time domain convolution = frequency domain multiplication)

this shifts the pass band from Ω = 0 to Ω0 = +- Ω0

Question 10

What is the moving average impulse response

Answer 10

Question 11

Describe the basis of the fourier transform method

Answer 11

emphaises on seros and poles

Take the transform equation(X(Ω)) and the inverse function rewritten to describe a LTI Processor rather than a signal (h[n])

Starting with H(Ω) and deriving the impulse response h(n)

Question 12

Fourier transform method equations

Answer 12

Question 13

Describe what truncation is

Answer 13

truncation is where you just cut off a signal. The effect is you get sidelobes of a certain size (dB)

Question 14

Decribe an idea low pass filter (graphic)

Answer 14

Question 15

DEscribe 3 different frequanecy responses to an ideal linear phase band pass filter . Talk through each one

Answer 15

Question 16

Describe windowing in both the time domain and the freqency domain

Answer 16

Question 17

Describe how the dB system is used and which are the important log values that correspond to it.

Answer 17

Question 18

Describe how side lobes work and the ideal value for them to be in a filter design

Answer 18

ideally below -40dB (0.01)

Question 19

What is the spectrum given by a rectangular window?

Answer 19

Question 20

Triangle window spectrum and its technical name

Answer 20

Barlett

Question 21

Hamming window definition

Answer 21

Question 22

von Hann window definition

Answer 22

Question 23

What does the kaiser window give the design the ablility to do?

Answer 23

It gives the designer the ablility to control how much ripple the filter has. As shown in this image

Question 24

Kaiser window definition

Answer 24

Question 25

Describe what happens with the Eqiripple filter

Answer 25

This is where the designer can choose exactly what parameters the signal should ripple against

Question 26

What are the corresponding formulas relating to the the equiripples filter

Answer 26

Question 27

What are the difference betwen a recursive and non recurisve filter and what are the disadvantages and advantages of each other

Answer 27

Recursive (typically IIR) = feedback - alot less terms and therefore memory required to create filters of the same performance as there corresponding non-recurisve design. They can be integraters non-recursive are always FIR (filter Impulse Response). they are split into window designs. They are capable of being differentiators..

Question 28

Recursive filters transfer function difference equation definition and pole zero description.

Answer 28