Linearity and Frequency responses

Question 1

What is meant by “black box” analysis?

Answer 1

-It does not matter how a system changes a signal, but what it does
-Compare output to input

Question 2

What is an LTI?

Answer 2

Linear time-invariant system

Question 3

What are two facts of LTI systems?

Answer 3

-LTI systems can be completely characterised by its response to sinusoids
-Any complex wave can be made by adding up sinusoids of varying frequency, amplitude and phase

Question 4

A sinusoidal input to an LTI is going to what kind of output?

Answer 4

A sinusoidal output of the same frequency

Question 5

Which systems are LTI?

Answer 5

-1,2 and 3
-4 and 5 are not LTI because they are not operating at the same frequency

Question 6

If you know the response of a system to a sinusoid of a particular frequency, amplitude and phase what can you predict?

Answer 6

The response of the system to another sinusoid of the same frequency

Question 7

What is meant by linearity?

Answer 7

Homogeneity + Additivity

Question 8

What is meant by homogeneity?

Answer 8

-Change in the size of the input is matched by the same change in the size of the output
-If you double the size of the input signal it also doubles the size of the output signal while halving the input signal will halve the size of the output signal

Question 9

How do we test for homogeneity?

Answer 9

1. Present a sinewave of a particular frequency to the system
   -Measure the level of the output signal as you vary the level of the input signal
   -Plot the level of the output signal on the y axis and the level of the input signal on the x axis
   -If the input/ output function is a straight line it means the system is homogeneous

Question 10

What is additivity?

Answer 10

-Adding two waves together
-The output of a system to two separate input signals added together is the same as the separate output signals for each of the inputs on their own, added together

Question 11

How do you add two waveforms together?

Answer 11

Add the amplitude values at each point in time

Question 12

If you sum two waveforms together what stays constant?

Answer 12

Their pitch

Question 13

What is this equation representing?

Answer 13

-The concept of additivity
-Signals are not interacting- can simply add them together to achieve the same output you would get separately

Question 14

Describe this image

Answer 14

Two different inputs generating two separate outputs added together will have the same output when summed as inputs

Question 15

What is time-invariance?

Answer 15

-LTI systems are time-invariant
-This means that delaying the input signal by a particular amount for a pair of input and output signals delays the output signal by the same amount
-I.e. the system’s behaviour does not change in time

Question 16

Describe this image

Answer 16

-The inputs generate the same output regardless of the delay

Question 17

What is meant by a frequency response?

Answer 17

The response of a system to sinusoidal inputs of different frequencies

Question 18

What are the three parameters that sinusoids vary on?

Answer 18

Frequency, amplitude and phase

Question 19

How can you use a sinusoid to measure an amplitude response in an LTI system?

Answer 19

1. Choose a constant sound level
2. For each frequency feed the input sinusoid to the system and measure the level at output
3. Calculate the response by measuring the ratio of output signal to input signal (output/input)- also known as gain
4. Calculate the delay between the output and input and convert to phase

Question 20

What kind of scale is used for frequency response?

Answer 20

-A logarithmic scale (dB)

Question 21

How do you express amplitude ratio in dB?

Answer 21

20 x log (output amplitude/ input amplitude)

Question 22

How is dB SPL calculated?

Answer 22

20 log (? Pa/20 x10-6 Pa)
-This expresses the output level in dB in relation to the input level

Question 23

What is the amplitude response?

Answer 23

The change made by a system to the amplitude of a sinewave, specified over a range of frequencies