Linearity and Frequency responses Flashcards
What is meant by “black box” analysis?
-It does not matter how a system changes a signal, but what it does
-Compare output to input
What is an LTI?
Linear time-invariant system
What are two facts of LTI systems?
-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
A sinusoidal input to an LTI is going to what kind of output?
A sinusoidal output of the same frequency
Which systems are LTI?
-1,2 and 3
-4 and 5 are not LTI because they are not operating at the same frequency
If you know the response of a system to a sinusoid of a particular frequency, amplitude and phase what can you predict?
The response of the system to another sinusoid of the same frequency
What is meant by linearity?
Homogeneity + Additivity
What is meant by homogeneity?
-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
How do we test for homogeneity?
- 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
What is additivity?
-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
How do you add two waveforms together?
Add the amplitude values at each point in time
If you sum two waveforms together what stays constant?
Their pitch
What is this equation representing?
-The concept of additivity
-Signals are not interacting- can simply add them together to achieve the same output you would get separately
Describe this image
Two different inputs generating two separate outputs added together will have the same output when summed as inputs
What is time-invariance?
-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
Describe this image
-The inputs generate the same output regardless of the delay
What is meant by a frequency response?
The response of a system to sinusoidal inputs of different frequencies
What are the three parameters that sinusoids vary on?
Frequency, amplitude and phase
How can you use a sinusoid to measure an amplitude response in an LTI system?
- Choose a constant sound level
- For each frequency feed the input sinusoid to the system and measure the level at output
- Calculate the response by measuring the ratio of output signal to input signal (output/input)- also known as gain
- Calculate the delay between the output and input and convert to phase
What kind of scale is used for frequency response?
-A logarithmic scale (dB)
How do you express amplitude ratio in dB?
20 x log (output amplitude/ input amplitude)
How is dB SPL calculated?
20 log (? Pa/20 x10-6 Pa)
-This expresses the output level in dB in relation to the input level
What is the amplitude response?
The change made by a system to the amplitude of a sinewave, specified over a range of frequencies
