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SLP > 02 - Speech Signal Processing > Flashcards

02 - Speech Signal Processing Flashcards

1
Q

What is a signal?

A

A varying physical quantity that conveys information or carries energy. In this course we primarily use continuous-time signals

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2
Q

What is sampling?

A

Sampling is the process of converting a continuous-time signal into a discrete-time signal.

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3
Q

What is the Nyquist-Shannon sampling theorem?

A

The sampling rate should be greater than twice the highest frequency component (in the original signal).

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4
Q

What is a periodic signal?

A

A signal that remains unchanged by a temporal shift. In other words, the signal (sound signal e.g.) is constant and repeated in a cycle. For example the sound ‘a’ is a periodic signal.

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5
Q

What is a discrete-time unit impulse?

A

It is a discrete-time signal that has a value of 1 at time=0 and 0 everywhere else. Also known as the Kronecker delta-function.

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6
Q

What is a discrete-time unit-step?

A

A signal that has a constant value of 1 for all time indices greater than or equal to zero and a value of 0 for all time indices less than zero.

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7
Q

What is a discrete-time complex exponential signal?

A

It is a signal that can be represented in rectangular and polar coordinates.

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8
Q

TOBEDELETED:
A discrete-time signal is defined by the equation. Check if the
signal is periodic and, if so, compute its fundamental period.

A

See slide 106 in the AllSlides.

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9
Q

When we talk about ‘systems’ in SLP, what do we mean?

A

A system is simply a process that takes an input signal and produces an output signal.

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10
Q

What is a ‘linear and time-invariant’ (LTI) system?

A

It is a system that brings together the properties of additivity, homogeneity and time-invariance.

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11
Q

What is a convolution sum and why do we use it?

A

A convolution sum is used to combine two signals into one new signal. We use it to compute the response to any input signal if we know h(n) which is the impulse response of the LTI system.

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12
Q

The discrete-time complex exponential signal is an eigenfunction of which system?

A

A discrete-time LTI system.

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13
Q

What is a transfer function?

A

In signal processing, the transfer function is a mathematical representation of how an input signal is transformed into an output signal by an LTI system. (We often use the z-transform)

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14
Q

What is a difference equation?

A

A difference equation is a mathematical equation that describes the evolution of a sequence of values over time. It relates the value of a variable at one point in time to its value at a previous point in time, as well as any inputs or external factors that may affect it.

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15
Q

What is the Kronecker delta function ( δ(n) )?

A

It is a discrete-time signal that has a value of 1 at time=0 and 0 everywhere else. Also goes under the name of ‘discrete time unit-impulse’.

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16
Q

What does DFS stand for?

A

Discrete Fourier Series

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17
Q

What is a ‘frequency response’?

A

It is a measure of how a system responds to different frequencies of input signals.

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18
Q

What is a DTFT?

A

A Discrete-Time Fourier Transform.

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19
Q

In words, what is the ‘Convolution property of the DTFT’?

A

The convolution property of the Discrete-Time Fourier Transform (DTFT) states that the DTFT of the convolution of two discrete-time signals is equal to the product of their individual DTFTs. In other words, convolving two signals in the time domain corresponds to multiplying their respective frequency representations in the frequency domain. This property is fundamental for analyzing the frequency characteristics of signals and systems in the context of the DTFT.

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20
Q

In words, what is the ‘z-transform’?

A

The z-transform is a mathematical technique used to analyze discrete-time signals and systems in the frequency domain. Similarly to the discrete-time Fourier transform (DTFT), it converts time-domain sequences of discrete samples (a discrete-time signal) into complex numbers, which can be used to represent the frequency response of a system or signal.

21
Q

What is the z-transform a generalization of?

A

The z-transform is a generalization of the discrete-time Fourier transform (DTFT) that converges for a larger class of signals.

22
Q

The z-transform is similar to the Laplace transform, but what is it usef specifically for?

A

The z-transform is similar to the Laplace transform, which is used for continuous-time signals and systems, but is specifically designed for discrete-time signals and systems.

23
Q

What does the z-transform allow us to analyze?

A

The z-transform allows for the analysis of stability, causality, and other properties of discrete-time systems and signals.

24
Q

We might use the z-transform to time shift a signal. Why?

A

It allows for analyzing and manipulating signals in the z-domain by introducing time delays or advances in the time domain.

25
Q

What does the DFT do?

A

In signal processing, the discrete Fourier transform takes a finite-duration discrete-time signal and converts it to a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT).

26
Q

Why is the symmetry property of the DFT useful?

A

It is useful because we can limit the range of the spectrum to half of the sampling frequency without loss of information.

27
Q

Why is circular convolution useful?

A

Circular convolution is used when we are dealing with a signal that exhibits periodic behaviour and provides a more accurate analysis.

28
Q

What is the property of circular convolution with DFT?

A

The product of two DFT’s of order N is the DFT of the circular convolution of the two discrete-time signals.

29
Q

What is the Fast Fourier Transform (FFT)?

A

In signal processing, the fast Fourier transform (FFT) is an algorithm that efficiently computes the discrete Fourier transform (DFT)of a discrete-time signal, or its inverse.

30
Q

How does the Fast Fourier Transform (FFT) achieve its efficiency?

A

It splits the computation of the DFT into successive halves, and therefore we get the same result with better efficiency.

31
Q

What is the ‘Ideal Low-Pass Filter’?

A

It is a filter that passes all frequency components of a signal below the cutoff frequency and blocks all frequencies above that threshold.

32
Q

Why do we use windowing functions?

A

They are applied to modify the characteristics of a signal before performing spectral analysis.

33
Q

What is the Rectangular Window?

A

The window is simple and has a value of 1 withing an interval and 0 outside of it.
It provides equal weights to all samples within the window.
The result is a wide lobe and a lot of spectral leakage.

34
Q

When do we use the Rectangular Window?

A

The rectangular window is typically used when sharp frequency resolution is required, but the presence of sidelobes and spectral leakage can cause distortions in the frequency domain.

35
Q

What is the Hann Window?

A

The Hann window, also known as the raised cosine window, tapers the edges of the rectangular window to reduce spectral leakage and sidelobes. It has a smoother transition at the edges, resulting in better frequency resolution and reduced distortion.

36
Q

When do we use the Hann Window?

A

The Hann window is often used when moderate frequency resolution and lower sidelobe levels are desired.

37
Q

What is the Hamming Window?

A

The Hamming window is another type of window function that provides improved sidelobe attenuation compared to the Hann window. It has a more significant tapering effect at the edges, resulting in reduced spectral leakage and better frequency resolution.

38
Q

When do we use the Hamming Window?

A

The Hamming window is commonly used when moderate to high frequency resolution is required, along with good sidelobe suppression.

39
Q

What is the Blackman Window?

A

The Blackman window is a window function with excellent sidelobe suppression. It provides the highest level of attenuation of sidelobes among the discussed windows. The Blackman window has a more complex shape with multiple tapering components, resulting in improved frequency resolution and reduced spectral leakage.
Rectangular –> Hanning –> Hamming –> Blackman

40
Q

When do we use the Blackman Window?

A

It is typically used when high-frequency resolution, low sidelobes, and good spectral accuracy are necessary.

41
Q

What do we mean with sidelobe suppresion?

A

Sidelobe suppression refers to the process of reducing the amplitude or energy of these sidelobes, making them smaller relative to the main lobe. It aims to minimize the unwanted artifacts and improve the accuracy of spectral analysis.

42
Q

What is ‘attenuation’?

A

Attenuation is a term that describes the reduction of strength (amplitutde or energy) in a signal.
Higher attenuation indicates a greater reduction in sidelobe amplitudes, resulting in a cleaner and more focused frequency representation.

43
Q

What is a Finite Impulse Response (FIR)?

A

A finite impulse response (FIR) system is a type of a discrete-time LTI system where the output depends only on a finite number of input samples. It is also known as an FIR filter.

44
Q

What is an Infinite Impulse Response (IIR)?

A

An infinite impulse response (IIR) system is a type of a discrete-time LTI system where the output depends both on a finite number of input and output samples. It is also known as an IIR filter.

45
Q

Summary question: ‘Signals’ refers to?

A

A function of time that conveys information

46
Q

Summary question: ‘Systems’ refers to?

A

Any system that takes an input signal and produces an output signal.

47
Q

Summary question: ‘Continuous Frequency Representations’ refers to?

A

Fourier Seires, Fourier transform, z-transform

48
Q

Summary question: ‘Discrete Frequency Representations’ refers to?

A

Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT)

49
Q

Summary question: ‘Digital Filters and Windows’ refers to?

A

Slices in time (windowing) and in frequency (filtering).

SLP (9 decks)

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