Week 9 FIR filters

Question 1

Whats a phasor equal to?

Answer 1

A complex amplitude

Question 2

Examples of some common values?

Answer 2

• j has angle of 0.5pi
• -1 has angle of pi
• • j has angle of 1.5pi
• also, angle of -j could be -0.5pi = 1.5pi -2p
• because the PHASE is AMBIGUOUS

Question 3

Describe values for complex exponentials:

Answer 3

• Real part is cosine
• Imaginary part is sine
• Magnitude is one

Question 4

What can we call about phase from frequency?

Answer 4

• Positive freq. has phase = -0.5p

* Negative freq. has phase = +0.5p

Question 5

• Is negative frequency real?

Answer 5

• Doppler Radar provides an example
• Police radar measures speed by using the Doppler shift principle
• Let’s assume 400Hz 60 mph
• +400Hz means towards the radar
• -400Hz means away (opposite direction)

Question 6

Whats the expression for periodic functions?

Answer 6

x(t) = x(t+T)

Question 7

Definition of T:

Answer 7

Time period

Question 8

Definition of k:

Answer 8

Integer

Question 9

Periodic signals can only have?

Answer 9

f(k) = f(0)k

f(0) = 1/T

Question 10

Define fundamental frequency f(0)?

Answer 10

Largest

Question 11

Define fundamental time period T(0)?

Answer 11

shortest

Question 12

Examples of digital filtering?

Answer 12

• CONCENTRATE on the COMPUTER
 • PROCESSING ALGORITHMS
• SOFTWARE (MATLAB)
• HARDWARE: DSP chips, VLSI
• DSP:
DIGITAL SIGNAL PROCESSING

Question 13

Define a finite impulse response system?

Answer 13

Finite impulse response (FIR) filters are systems for which each output value is the sum of a finite number of weighted values of the input sequence.

Question 14

Examples and definition of discrete time systems:

Answer 14

EXAMPLES:
– POINTWISE OPERATORS
§ SQUARING: y[n] = (x[n])2 – RUNNING AVERAGE
§ RULE: “the output at time n is the average of three consecutive input values”

Question 15

How can finite impulse filters be classed as a 3 point running average?

Answer 15

• The FIR filter is a generalization of the idea of running average.
• To be specific, consider a 3-point running average where each sample of the output sequence is the sum of three consecutive input sequence samples divided by three

Question 16

General FIR filter

Answer 16

• FILTER ORDER is M
• FILTER LENGTH is L = M+1
– NUMBER of FILTER COEFFS is L

Question 17

What do casual systems use?

Answer 17

-Past values