Signal Processing Flashcards
Define Peak to Peak pressure
Maximum difference between the highest and lowest pressure levels in the signal
Lpp = 20log10 [ Ppp/P0]
In dB
Define RMS pressure
Root mean square value of pressure fluctuations in the signal
Define Peak Rarefactional pressure
The lowest pressure level reached during the rarefaction phase of a signal
Define Peak Compressional pressure
The highest pressure level reached during the compression phase of a signal
Define Sound Pressure Level (SPL)
Measurement of the intensity or loudness of sound.
It is basically the RMS in underwater acoustics
What is peak pressure?
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
What is Sound exposure?
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
What is Sound Exposure Level?
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
Name the common acoustic field metrics
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
How do you define when SEL has ‘stopped’?
Put threshold on the gradient
So you can say its not growing at a fast enough rate so it is ‘flat’
What can negative pressure cause?
Tissue damage
Define the Nyquist-Shannon theorem
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
What if you sample a signal with greater than half the sample rate?
The under sampled signal will be reproduced at a lower frequency
Define Aliasing
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.
Name affects of Aliasing
Frequency distortion
Loss of Information
Unwanted noise
How to avoid Aliasing
Add a low pass filter - put at the top of your bandwidth of interest
Increase the sampling rate
Define Downsampling
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
How to work out the frequency resolution?
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
What is FFT?
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
What is DFT?
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.
Why is FFT output symmetrical and reversed?
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
What is an Anti-aliasing filter for?
Remove high frequency components from a signal before sampling ( ADC)
What is Amplitude scaling?
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
Why are FFTs are always a power of 2?
it will be highly optimised for these lengths power of 2.
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
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
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
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
Notes on Spectral leakage and frequency bins
Perfect match = perfect response
Not perfect = Overlapping bins
Sum of areas under curve should be the same
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
Define a Boxcar Window
Rectangular / Boxcar
Multiples everything essentially by 1
So basically nothing happens
E.g. Boxcar Window (256)
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 ]
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
Define Truncating
Process of disregarding a portion of a signal beyond a specified point/ threshold
Reducing length/magnitude
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
What affect does adding overlaps to an FFT have?
To get more accuracy
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)
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
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
What is Spectral level?
straight output
RMS value
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
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
What is a Periodogram
a plot / estimation of the power spectral density of a signal
can see distribution of signal power across different frequencies
List some examples of noise events
Clanking
Rattle - broadband signal - wide range of frequencies that span across a broad spectrum
Squeak
Banging
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
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
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
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
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
What is Cross- correlation?
