03 - Speech Signal Representations

Question 1

What is the ‘Zero-Crossing Rate’?

Answer 1

It is the rate at which a signal crosses the horizontal (x) axis or the zero level.

Question 2

When is it useful to check the Zero-Crossing Rate?

Answer 2

The Zero-Crossing Rate can be useful to check in many scenarios. It contains information such as the frequency content and overall changes in the signal. We often check it during speech analysis.

Question 3

What does the ‘Autocorrelation’ measure?

Answer 3

The similarity of a signal compared to its time-delayed self.

Question 3

What does the term ‘Windowing’ refer to?

Answer 3

Answer from research:
Windowing is the process of multiplying a frame with a function so that the signals characteristics are modified, so that the amplitude of the signal is gradually reduced towards the edge of the window. It is often used on frames to achieve a quasi-stationary analysis.

From the slides (I partially disagree with this):
It is the process of splitting the input signal into temporal segments where the signal can be considered quasi-stationary. That is, not really stationary, but in the essence of the analysis, they are.

Question 4

What does the term ‘Frame’ refer to?

Answer 4

It is a continuous segment of a signal that is isolated for analysis and processing.

Question 5

What is the Overlap-add algorithm?

Answer 5

It is an algorithm that describes the process of recombining overlapping frames of a signal after some processing.

Question 6

What are the steps of the Overlap-add algorithm (think LAB 2)?

Answer 6

1. Input signal is windowed into frames of a certain frame length with a certain interval (hop length)
2. We compute the output from the input frame
3. We apply a window to the output frame (for example Hamming)
4. We recombine the overlapping output frames

Question 7

Why do we use the Overlap-add algorithm?

Answer 7

It is an efficient computation of the convolution of two signals by breaking them into smaller segments, convolving each segment separately, and then combining the results.

Question 8

What is the Short-Time Fourier Transform?

Answer 8

The short-time Fourier transform is a type of Fourier analysis used to determine the frequency content of a signal over short, fixed-length time intervals.

Question 9

What is a ‘Spectrogram’?

Answer 9

A spectrogram is a visual representation of the frequency content of a signal over time. It is a plot that displays the intensity of different frequencies of a signal as they change over time, typically represented as a heat map or color map. The x-axis is time and the y-axis is frequency (Hz)

Question 10

What is a Source-Filter Model?

Answer 10

In speech signal processing, the source filter model is a mathematical model that represents the speech signal by a combination of a sound source with a linear acoustic filter.

Question 11

What is a ‘Second Order All-Pole Filter’?

Answer 11

It is a system that has two poles and no zeros in the transfer function.

Question 12

What is ‘Linear Prediction’?

Answer 12

Linear prediction is a method that tries to predict a signal sample using a linear combination of the signal’s past samples.

Question 13

What is the ‘residue’ of Linear Prediction?

Answer 13

It is the prediction error, sometimes referred to as the residuals in other models.

Question 14

What does Linear Prediction Optimization refer to?

Answer 14

The minimization of the energy of the prediction error.

Question 15

What is a ‘cepstrum’?

Answer 15

The cepstrum is defined as the inverse discrete Fourier transform (DFT) of the log magnitude of the DFT of a signal.

Question 16

What is the ‘mel frequency spectrum’?

Answer 16

The mel spectrum is a frequency representation where the frequencies are scaled to better match the human perception of sound. This scaling is accomplished using the mel frequency scale, which is a non-linear transformation of frequency that emphasizes lower frequencies more than higher frequencies.

Question 17

Why do we transform using the mel frequency scale?

Answer 17

It is easier for human perception.

Question 18

What are the steps of the ‘Mel-Frequency Cepstral Coefficients’ (MFCC) ?

Answer 18

1. We compute the DFT (Discrete Fourier Transform) of the signal
2. We compute the log-mel-spectrum (simply the log of the mel-spectrum)
3. We compute the DCT (Discrete Cosine Transform) of the log-mel-spectrum

Question 19

The Linear Prediction Coefficients (LPC) are what?

Answer 19

The linear prediction coefficients are a set of coefficients that are used in linear prediction analysis to estimate future values of a time series based on past observations.

Question 20

What is the Discrete Cosine Transform (DCT)?

Answer 20

The discrete cosine transform is a frequency representation similar to the Fourier transform, but it uses only real-valued functions and is more efficient for processing data that has symmetric properties.

Question 21

MFCC is an abstract domain that is difficult to interpret. True or false?

Answer 21

True

Question 22

The log-mel spectrum is not perceptually motivated. True or false?

Answer 22

False

Question 23

The Discrete Cosine Transform decorrelates sequentially correlated data. True or false?

Answer 23

True

Question 24

MFCC’s is an efficient representation for computation. True or false?

Answer 24

True

Question 25

We can obtain dynamic information with delta and delta-delta MFCC’s. True or false?

Answer 25

True

Question 26

Summary question: Time-Domain Features refers to?

Answer 26

Root Mean Squared (RMS), zero-crossing rate and auto-correlation.

Question 27

Summary question: Windowing refers to?

Answer 27

Handling non-stationary signals.

Question 28

Summary question: Source-Filter Model and LPC (Linear Predictive Coding) refers to?

Answer 28

Estimation of vocal tract filter and excitation (making the signal more active).

Question 29

Summary question: Frequency Representations refers to?

Answer 29

Log-spectrum, log-mel-spectrum, cepstrum and MFCC’s.

Question 30

What is ‘formant’?

Answer 30

In speech processing, a formant is a resonance in the vocal tract that results in a peak of energy in the speech signal at a particular frequency.

Formants are important for distinguishing between different vowel sounds and correspond to high-energy areas of the spectrum of a vowel.

Question 31

What is a ‘cascade combination’?

Answer 31

In signal processing, the cascade combination of two systems means that the output of the first system is fed as input to the second system.