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Signal Processing Flashcards

(50 cards)

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1
Q

Define Peak to Peak pressure

A

Maximum difference between the highest and lowest pressure levels in the signal

Lpp = 20log10 [ Ppp/P0]
In dB

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2
Q

Define RMS pressure

A

Root mean square value of pressure fluctuations in the signal

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3
Q

Define Peak Rarefactional pressure

A

The lowest pressure level reached during the rarefaction phase of a signal

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4
Q

Define Peak Compressional pressure

A

The highest pressure level reached during the compression phase of a signal

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5
Q

Define Sound Pressure Level (SPL)

A

Measurement of the intensity or loudness of sound.

It is basically the RMS in underwater acoustics

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6
Q

What is peak pressure?

A

p_peak = max|p(t) |

Maximum pressure level reached in a signal.

Lpeak = 20log10 [Ppeak/P0]
In dB

Aka Zero-to-peak sound pressure level

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7
Q

What is Sound exposure?

A

Cumulative sound energy over time.

E = integral between 0 and T ( p^2 (t)) dt

This is a metric of energy

Don’t divide by time

Signal will get bigger and bigger

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8
Q

What is Sound Exposure Level?

A

Sound Exposure Level (SEL) is a measure of the cumulative sound energy over a specified duration, commonly used to assess potential noise impact or risk.

Used in airborne acoustics as well

Useful for pulses as energy in signal is considered

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9
Q

Name the common acoustic field metrics

A

Peak pressure
Peak-Peak pressure
Sound Exposure Level (SEL)
Sound Pressure Level (RMS)

Example:
pk-pk: 189.5 dB re 1 μPa
pk: 183.5 dB re 1 μPa
SPL: 172.5 dB re 1 μPa
SEL: 164.1 dB re 1 μPa^2·s

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10
Q

How do you define when SEL has ‘stopped’?

A

Put threshold on the gradient
So you can say its not growing at a fast enough rate so it is ‘flat’

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11
Q

What can negative pressure cause?

A

Tissue damage

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12
Q

Define the Nyquist-Shannon theorem

A

The minimum number of samples required to faithfully reproduce at continuous signal is 2 per wavelength

Therefore the maximum bandwidth is the sample rate / 2

Minimum is 2 samples per maximum
Wavelength you want to detect i.e.

Example
Signal frequency = 1500Hz
Sample frequency = 80000 Hz

Well sampled

Signal frequency = 1500Hz
Sample frequency = 8000 Hz

OK as around 5 samples per wavelength

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13
Q

What if you sample a signal with greater than half the sample rate?

A

The under sampled signal will be reproduced at a lower frequency

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14
Q

Define Aliasing

A

Aliasing is a phenomenon in signal processing where high-frequency components are incorrectly represented as lower frequencies, leading to distortion or loss of information in the signal.

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15
Q

Name affects of Aliasing

A

Frequency distortion

Loss of Information

Unwanted noise

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16
Q

How to avoid Aliasing

A

Add a low pass filter - put at the top of your bandwidth of interest

Increase the sampling rate

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17
Q

Define Downsampling

A

Reducing sampling rate/resolution of a signal by discarding/ averaging samples

Can be to reduce computational complexity or storage requirements

A digital filter is needed before downsampling

You will be at risk of aliasing

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18
Q

How to work out the frequency resolution?

A

Frequency resolution (df)
= Sample rate / N

where n is the number of samples

Limit the value of N
E.g. Dolphin clicks occur very quickly - only there for a very short amount of time so unecessary to have a large N

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19
Q

What is FFT?

A

Fast Fourier Transform

An efficient algorithm used to compute the DFT of a sequence or signal

Time domain signal is converted to frequency domain representation

Can see individual frequency components present in the signal and their respective magnitudes

Fout = abs(fft(y));

It can tell you the size of a sinusoid

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20
Q

What is DFT?

A

Discrete Fourier Transform

A mathematical algorithm that transforms a discrete-time signal or sequence from the time domain to the frequency domain

Allows analysis of the signal’s frequency components and their respective magnitudes.

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21
Q

Why is FFT output symmetrical and reversed?

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A

Due to complex conjugate symmetry property in DFT
Positive & Negative frequency components of a real valued signal are mirrored and have equal magnitude but opposite phases

Can shift the two halves and offset by Fs/2

22
Q

What is an Anti-aliasing filter for?

Study These Flashcards
A

Remove high frequency components from a signal before sampling ( ADC)

23
Q

What is Amplitude scaling?

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A

Modifying the magnitude / intensity of a signal.
Change amplitude but preserve relative proportions

Amplitude needs to be scaled by the sample rate

Fout_scaled = Fout / N
where N is size of FFT

24
Q

Why are FFTs are always a power of 2?

Study These Flashcards
A

it will be highly optimised for these lengths power of 2.

25
What is Zero padding?
Adding extra zero valued samples to the end of a signal before a Fourier Transform / any spectral analysis Length of signal increased, content is unchanged Increases the frequency resolution of the analysis while maintaining original time domain information It's interpolation It can be misleading
26
What is Spectral Leakage
Energy from a specific frequency is a signal spreads into neighbouring frequency bins during DFT Causes inaccuracies in the spectral representation
27
What is the bin centre frequency
The midpoint frequency value within a frequency bin in a DFT/ FFT Represents the representative frequency of that speciific bin
28
What is a frequency bin
The discrete division / interval that a frequency spectrum is divided into during spectral analysis Each bin represents a specific range of frequencies If a bin is really wide - df is bigger - x will be greater so more energy through
29
Notes on Spectral leakage and frequency bins
Perfect match = perfect response Not perfect = Overlapping bins Sum of areas under curve should be the same
30
What is a window function?
A mathematical function applied to a signal before performing spectral analysis Its to reduce spectral leakage Improve the accuracy of frequency domain representation by tapering the signal at its edges
31
Define a Boxcar Window
Rectangular / Boxcar Multiples everything essentially by 1 So basically nothing happens E.g. Boxcar Window (256)
32
How to compensate for a window function when calculating the RMS?
No window: RMS = √[ Σ ( 1/N |FFT| (k)| )^2 ] U = √ [1/N Σwin(n)^2 ] U is a correction factor sum of the square of the window values RMS_window = 1/U * √[ Σ ( 1/N |FFT| (k)| )^2 ]
33
Define a Hanning Window
Multiply every element in the time domain by a value in the window. E.g. if window is from 0 to 1 first value multiple by 0 middle value multiple by 1 last value by 0 Like a bell curve E.g. Hanning Window (256) where 256 is the block of time good for small signals next to a large one helps tell if you have contamination max y value is lower, shape changes skirt may not be as wide energy isn't spreading out into the other energies
34
Define Truncating
Process of disregarding a portion of a signal beyond a specified point/ threshold Reducing length/magnitude
35
Define a Spectrogram
A visual representation of the frequency content of a signal over time Intensity/ colour of each point in the graph indicates magnitude / power of the corresponding frequency component at a specific time instant Each vertical line of pixels is an FFT Higher n value - smaller frequency resolution - will start interpolating values in between e.g. zero padding will look like you get more values but you are't
36
What affect does adding overlaps to an FFT have?
To get more accuracy
37
Name properties of an FFT and Spectrogram
Sample Rate – (fs in Hz) Window size (N = 128, 1024, etc.) Frequency resolution (Δf = fs/N) Window function (Hanning, Hamming, etc.) Overlap – how far each window overlaps Calibration – is your transducer response flat? Processor gain Spectral density (i.e. dB re 1 μPa2/Hz or dB re 1 μPa/√Hz) Spectral level (i.e. dB re 1 μPa)
38
What does Spectral density allow you to do?
You can compare data from one sample rate with data of a different sample rate directly If you are looking at coherent noise Divide energy in the bin by width of bin for normalising into spectral density
39
What is Processor gain?
1/N like an amplifier needed if signal is long enough Signals need to be continous signal will appear out of noise
40
What is Spectral level?
straight output RMS value
41
What is temporal smearing?
the blurring or loss of time-domain details in a signal or waveform often caused by the effects of filtering or signal processing operations that introduce a delay or reduce time resolution Stretching time
42
What is Welch Averaging?
--> method of spectral estimation --> divide signal into overlapping segments --> apply a window function to each segment --> compute the periodogram of each segment --> average the periodograms its for obtaining a smoother more reliable estimate of the signal's power spectral density e.g. do 28 FFTs instead of 1 big one allows you to see underlying trend reduces incoherent noise
43
What is a Periodogram
a plot / estimation of the power spectral density of a signal can see distribution of signal power across different frequencies
44
List some examples of noise events
Clanking Rattle - broadband signal - wide range of frequencies that span across a broad spectrum Squeak Banging
45
What are Octave bands?
AKA frequency bands musical scales use octave bands there is a doubling/halving ration between upper and lower limits lower frequency = f1 = f0/√2 upper frequency = f2 = f0 x √2 f2 = 2 x f1 Bandwidth = f2 - f1 need high resolutions are low frequencies low frequencies take longer to exist human hearing is based on 3rd of an octave provide a logarithmic and perceptually uniform representation of the frequency content of a signal
46
What are Octave and Third Octave Band filters?
Specialised filters they divide the frequency spectrum into specific frequency bands Octave band filters - split spectrum into octave bands - doubling/ halving ratio Third Octave band filters - for narrower subdivisions with a tripling or one0third ratio
47
What are Third Octave Bands?
TOb AKa Deci decade bands - for more detailed and refined assessment of frequency - upper freq is ~1.26x the lower freq - narrower subdivisions that Octave bands - accuracy is poorer at high freqs
48
What is Spectral Density?
dB re 1μPa/√Hz Spectral density = Spectral level - 10log10(bandwidth in Hz) i.e. bandwidth it was recorded in distribution of power/ energy in a signal across different frequencies
49
What is Spectral Level?
dB re 1μPa measurement of magnitude/intensity of a specific frequency component/band within a signal - good for strong correlated narrow band tonal components
50
What is Cross- correlation?

Electronics (7 decks)

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