Week 10: frequency response of FIR filters

Question 1

What does the phase angle tell us?

Answer 1

The phase angle contains a lot of information about the signal

Question 2

What do we know about linear phase?

Answer 2

Linear phase: simple rigid shift in time (no distortion)

Question 3

What do we know about non linear phase?

Answer 3

Non-Linear phase: distortion as well as shift in time

Question 4

Why do bee log magnitude?

Answer 4

Allows details to be displayed in a wider dynamic range

Question 5

What are frequency selective filters?

Answer 5

Frequency selective filters modify the frequency response of the input. Amount of alteration depends only on the frequency of the signal.

Filters can pass or stop certain frequencies

Question 6

What can we also conclude about frequency selective filters?

Answer 6

Frequency selective filters modify the frequency response of the input Amount of alteration depends only on the frequency of the signal.

Filters can attenuate signals at a band of frequencies as
function of those frequencies.

Question 7

What do frequency selective filters do to the signal?

Answer 7

Attenuate a signal at a band of frequencies (as function of those frequencies) and/or change its phase.

Frequency selective filters modify the frequency response of the input Amount of alteration depends only on the frequency of the signal

Question 8

LTI systems with frequency responses chosen to:

Answer 8

LTI systems with frequency responses chosen to:

• Pass one or several bands of frequencies with little or no attenuation
• Stop or significantly attenuate frequencies outside those bands
  Cutoff frequencies: define boundaries between frequencies that are
  passed and those that are rejected, i.e. the frequencies in the passband
  and stopband.

Question 9

Whats an ideal frequency selective?

Answer 9

Ideal frequency selective filters: Lowpass

Perfect frequency and no phase distortion

Question 10

Time domain properties of ideal lowpass filter:

Answer 10

• The step response overshoot their long-term final values and exhibit oscillatory behaviour: ringing or Gibbs phenomenon

Question 11

Digital filtering:

Answer 11

• CONCENTRATE on the SPECTRUM
• SINUSOIDAL INPUT
• INPUT x[n] = SUM of SINUSOIDS
• Then, OUTPUT y[n] = SUM of SINUSOIDS

Question 12

Sinusoidal response:

Answer 12

• INPUT: x[n] = SINUSOID
• OUTPUT: y[n] will also be a SINUSOID
• Different Amplitude and Phase
• SAME Frequency

• AMPLITUDE & PHASE CHANGE
• Called the
FREQUENCY RESPONSE

Question 13

What should we do to exponents when putting expression into a certain form?

Answer 13

Find the average of the exponents

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