Yusuke Flashcards
What are the four sub-disciplines included in communication acoustics?
- Electro-acoustics and audio/speech signal processing
- Speech science and linguistics
- Human auditory perception
- Psychology of hearing (psychoacoustics)
What two electrical components does a sound signal consist of?
- DC (constant value; 0Hz)
- AC (sine wave of various frequencies)
When we analyse a sound signal, what is important to know?
It is important to know the amount of each frequency component in the signal
What is the amount of power usually measured by?
It is usually measured by the rms of amplitude
What are the two forms of a sound signal? And what are their domains?
- Waveform (ie time domain)
- Spectrum (ie frequency domain)
What are the two types of spectra in a sound signal? And what do they consist of?
- Amplitude spectrum (shows amplitude of sine waves at each frequency
- Phase spectrum (shows the phase of sine waves at each frequency (between -pi and pi))
What is the mathematical tool that derives the spectrum from the wave form, vice versa?
- Fourier analysis
What is the spectrum of a signal defined as mathematically? And what do we look at?
It ranges from -inf to inf. we look at f>0Hz
What are the frequency ranges for infrasound, audio sound and ultra sound?
Infra: <20Hz
Audio: 20-20kHz
Ultra: >20kHz
What frequency range can humans hear?
20Hz - 20kHz
What do we use an oscilloscope for?
To visualise the sounds waveform
What does digital mean in terms of signal processing and what are the two forms it is discretised in and what are their names? Draw a diagram to aid
Digital signal = analogue signal disretised in time (sampling) and value (quantisation). Diagram with sampling period and quantisation width lines for an analogue signal converted to digital
What is sampling a process of?
Converting a signal from continuous-time to discrete-time domain
What is the Shannon Sampling Theorem?
Continuous time signals with frequencies no higher than fmax can be reconstructed perfectly from its discrete-time signal if samples are taken at fs>2fmax
What is the nyquist rate?
Minimum sampling frequency to avoid aliasing (2fmax)
What is aliasing?
It is when spectral components (ie frequencies) above fs/2 are folded back
What is an anti-aliasing filter for?
It filters out the spectral components above fs/2. Often a low-pass filter
What is over-sampling?
Sampling at above the Nyquist rate
Why do we oversample instead of samplying at the nyquist frequency?
Because of limited roll-off (steepness) of the anti-aliasing filter
What is quantisation and what is assigned to each level of quantisation to acquire a completely digital signal
Discretisation of a signals value (amplitude)
What is pulse code modulation (PCM)? What two things does it apply?
It is a technique which expresses a signals values by a set of binary codes. It applies sampling and quantisation
What is quantisation noise? What determines resolution? What is the tradeoff?
Approximation of signal level by discretised values causes quantisation noise. Number of quantisation levels determines resolution. More levels means good resolution but more number of bits -> more memory.
What is the minimum sampling frequency for most acoustical applications and why?
Since audible frequency range is 20Hz - 20kHz, fs is >44.1kHz for most acoustical applications
What is the minimum sufficient resolution to cover dynamic range of human auditory system?
16bit
What is the tradeoff for sampling frequency?
Higher sampling freq reduces risk of aliasing, however it requires more memory
What does a spectral analysis entail? What is the first thing that must be calculated and how is it calculated?
It refers to a process that analyses properties of sound by looking into their spectrum.
The first process requires us to calculate the power spectral density (PSD) of the signal from the waveform
This is achieved by the fourier analysis
What is the relationship between the power spectral density and the mangitude of the spectrum
The PSD of the signal is the squared magnitude of the spectrum
What is another name for the fast fourier transform? What is it for and how does it differ from the fourier transform?
- AKA discrete fourier transform
- It is a digital implementation of the fourier analysis on a digital processor
- Fourier transform assumes infinite length, in order to use FFT, signal must be truncated (ie cut off the end)
What is the FFT length?
- Length of the truncated signal N
What is windowing and what is it applied to?
- windowing has non-zero values only for n=0,1,…,N-1
- truncated = windowed
- It is applied for truncation that limits the length of a signal within N samples
What are three commonly used windows? And draw the diagrams.
- Rectangular
- Hann (Hanning)
- Hamming (more specific decimals - tighter bell curve)
What is the short-time fourier transform used for? And how is it implemented?
- The STFT analyses non-stationary signals
- It divides the signal into short frames using windowing, then applies FFt to the signal of each frame
What are non-stationary signals?
Signal whose statistical properties (incl. PSD) vary from time to time.
What is a spectogram? and what transform is used to calculate it?
It is a representation of a time varying PSD of a signal. Short Time Fourier transform is used.
What determines frequency resolution in spectral analyses? Draw the PSD for a low N and high N pure tone wave
- The FFT length
- Low N diagram: normal distributed curve about f0
- High N diagram, sharper point at f0
What is the tradeoff when a spectogram is calculated?
- Between time and frequency resolutions:
A shorter window length improves time resolution, however a shorter window also decreases the truncated length which reduces frequency resolution
What is the trade-off between spectral distortion and frequency resolution?
- the shape of window function (ie rectangular, hann, hamming) affects the frequency resolution.
For the rectangular window, spectral distortion is relatively less, however frequency resolution is worse.
Which window types are most commonly used for audio?
- Hamming and Hann
What is a frequency band?
- Refers to a range of frequency in the spectral representation of signals
What are the seven audio frequency subbands?
- Sub-bass
- Bass
- Low midrange
- midrange
- Upper midrange
- Presence
- Brilliance
What is an octave band?
A band is said to be an octave in width when the upper band frequency is twice the lower band frequency
What is a 1/3 octave band?
A frequency band whose upper band frequency is the lower band frequency times 2^(1/3)
What is the characteristic of a linear system?
(a1x1 + a2x2)* linear system == lineara1x1 + lineara2x2
What is the characteristic of a time invariant system
-> delay -> time invariant system = -> time invariant system -> delay
Why do we focus on Linear Time-Invariant systems?
- Simplification of mathematical analysis
- Greater insight and understand of the systems behaviour
What is the word for two cascaded LTI systems that produce the same result
They are said to be commutative
What is the output of an LTI system when the input is a unit impulse?
Impulse response
What is the mathematical word that combines an input signal with the system’s impulse response?
Convolution
What is a RIR?
The room impulse response describes the properties of the acoustic transmission channel in a room from the sound source to the position where the sound is observed.
What is a free field?
Acoustic environment where no reflections are observed (ie anechoic)
If an arbitrary sound is emitted from a source, how can the observation at the microphone’s position be simulated?
By convoluting the source and RIR
What is frequency response? And how is it calculated?
- It shows how the system behaves (phase and amplitude) to a sinusoid of a particular frequency
- Typically complex valued
- Calculated by applying fourier analysis to the impulse response of the system
How is the output spectrum of a system calculated?
Multiplication of the input spectrum and the frequency response
What is the spectrum of a unit impulse?
Identical values for all frequencies
What does a filter do? What do most common filters do?
It removes an unwanted component or feature from a signal. Most commonly used to remove certain frequencies and/or reduce noise.
What are the four properties of a filter?
- Type - can be read by the shape of the amplitude response
- Passband - range of frequencies where the signal is passed through
- Stopband - range of frequencies where the signal is suppressed
- cut-off frequency - edge of the passband where there is a -3dB drop from passband gain
what are the four filter types? Draw the diagrams of each
- Low pass
- High pass
- Bandstop (stops frequencies within a given range)
- Bandpass
For the diagrams, remember non-vertical roll off
What are the two types of filters?
Finite impulse response (FIR) and infinite impulse response (IIR)