Signals and Systems (Frequency Domain)

Question 1

What is a crucial benefit of LTI system in frequency domain?

Answer 1

LTI system don’t change frequency content of signal
- allows for filtering of unwanted inputs (noise)

Question 2

What is filtering?

Answer 2

attenuation of particular frequency components in signal
- steepness of filter
- cut-off frequencies –> half of signal amplitude (-3dB)

Purpose: great rid of undesired signals (noises)

Question 3

What are some dis/advantages of active filters compared to passive filters

Answer 3

Adv
1. adjustable gain
2. low output impedance

Con:
1. limits high-freq operation (op-amps takes time to adjust to high-freq changes which results in lag)

Question 4

For which of the use cases would you do signal processing in frequency domain?
1. Finding duration of each ECG interval
2. Removing interfering inputs (additive noise)
3. Sampling an analog EMG signal

Answer 4

Removing interfering inputs (additive noise)

Question 5

What are some features of digital filters (4)

Answer 5

1. embedded in chip that operates on digital signals / comes as software solns
   2.programmable –> have high-precision and accuracy
2. requires A/D and D/A if used with the body (or any analog circuit)
3. slower than analog filters

Question 6

What are some features of FIR filters (3)

Answer 6

Type of digital feature called Finite Impulse Response
- have impulse response w/ finite duration in discrete time
- inherently BIBO stable
- symmetric in response (phase is linear –> preserve wave-shape of signal )

Question 7

How to use FIR filters to approximate ideal filters?

Answer 7

1. Windowing
   (ideal low pass filter has infinite impulse response –> by bandpassing for a symmetric range of frequencies –> generates finite impulse response)
2. Shifting
   (shift the symmetric range of frequencies such that it is definite for positive values)
   - creates a causal response that is required for real-time processing

Question 8

Compare and contrast the different types of filters (4)

Answer 8

Q = transition region (range of freq where bandpass transitions into bandstop)
A = attenuation (drop in signal strength)

1. Rectangular
   Q = 4pi / N
   A = -13dB
2. Bartlett
   Q = 8pi / N
   A = -27 dB
3. Hanning
   Q = 8pi / N
   A = -32 dB
4. Hamming
   Q = 8pi / N
   A = -43 dB
5. Blackman
   Q = -58dB
   A = 16pi / N

Ideal filter:
Q = low number (steeper transition)
A = large number (larger decrease in signal strength before the rippling)

Question 9

Nyquist Shannon Sampling theorm

Answer 9

To avoid aliasing:

sampling freq > 2 times the freq of the signal

(if ws = 2wm; still hard to recover because it requires perfect ideal LP filter