Digital Signal Processing (I)

I. Overview of digital signal processing 1. Digital Signal

(1) signal: a signal is a carrier for carrying information. Without information, the signal will be meaningless.

(2) digital signals: Signals processed by computers

1) Representation: X [N], which is a vertical line with a circle on the top.

2) digital signals can be expressed by pulse signals and step signals.

3) digital frequency and analog frequency conversion:

In the study of digital signal processing, many beginners are often confused about analog frequencies, digital frequencies, and their relationships, even some friends who have some knowledge about digital signal processing are also confused about this problem.
The frequency we usually refer to is the analog frequency, in Hz (HZ) or 1/second (1/S), unless otherwise specified ), the mathematical symbols are represented by F. This is because most of the signals in the real world are analog signals, and frequency is an important physical feature. The analog frequency in Hz represents the number of periods in which the signal changes per second. If the unit circle is used, as shown in 1, rotating a circle indicates that the signal changes for a period, then the simulated frequency indicates the number of signals rotated per second.
Another concept in the simulation frequency is to simulate the angle frequency. The mathematical symbols are commonly expressed by Ω, and the Unit is radian/s (rad/s ). From the perspective of the unit circle, the simulation frequency is the number of cycles of signal rotation per second, and the angle variation of each circle is 2PI. Obviously, the rotating F circle corresponds to the Radian of 2PI * F. That is:
Ω = 2PI * F (rad/s) (1)
Most digital signals are sampled from analog signals, and the sampling frequency is usually represented by FS. The more accurate digital frequency is called the normalized digital angle frequency, measured in radians (RAD), which are commonly expressed by ω. That is:
ω = 2PI * f/FS (RAD) (2)
The physical meaning is the number of radians that change between two neighboring sampling points, as shown in 1.
With formulas (1) and (2), we can switch between the analog frequency and the digital frequency at will. Assume that there is a sine signal X [N], its frequency f = 100Hz, its amplitude is A, and its initial phase is 0, the signal can be expressed as follows:
X (t) = A * sin (2 * pI * 100 * t)
Sample it with the sampling frequency fs = Hz. The resulting digital signal X [N] is:
X [N] = A * sin (2 * pI * 100 * n/Fs) = A * sin (0.4 * pI * n)
Obviously, the digital signal frequency is 0.4pi.
From the above discussion, we can see that the analog frequency of the two signals with identical digital frequencies may not be the same, because the sampling frequency must be considered here. This normalization brings convenience and confusion to understanding. Although the sampling frequency is often not explicitly displayed in digital signals, it serves as a bridge between analog signals and digital signals, which has a significant impact on the signal processing process.
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Deepdsp
Source: csdn
Original: 7272186

Matlab application:

 

T =. 05; % time scale: Minimum Time: sampling interval: maximum time value Y = sin (2 * t)-1; % cage function stem (T, Y) % draw Discrete Data Sequence

N =-; % Given Discrete point range y = 2 * exp (-0.5 * n); % given discrete value function stem (n, Y) % draw Discrete Data Sequence

 

(3) Digital Signal Processing: the signal is input into the computer for analysis and processing.

(4) Band-limited signal: the maximum frequency of the signal can be determined.

 

2. Digital Signal Processing System

(1) Signal Acquisition Method

Natural analog signals use various sensors to convert analog signals into analog electrical signals. For example, sound signals can be captured by microphones and converted into electrical signals. image signals can be captured and converted into electrical signals by cameras.

MATLAB Signal Acquisition

 

% ==============%%Start with Windows> program> attachment> % Entertainment> Recorder "The recorded voice is saved as a xx.wma file; ============ [x, FS] = audioread ('d: test.wma '); % Write File Path y = x (:, 1 ); % collect a single channel? Sound (Y, FS); % play sound figure; plot (y); xlabel ('time'); ylabel ('amplitude '); % draw a Time Domain Diagram

Program description:

[X, FS] = audioread ('d: test.wma '); % load the voice signal into the MATLAB simulation software platform, and place the sample value in vector X, FS indicates the sampling frequency (HZ ).

Y = x (:, 1); % single channel acquisition for dual-channel signals

(2) anti-aliasing filter

Many signals are not band-limited signals. If the maximum frequency is unknown, it is impossible to avoid mixing. To solve this problem, the signal is first filtered through the analog low-pass filter before sampling, so that the signal becomes a band-limited signal, and a sufficient sampling frequency can be used to avoid mixing.

Purpose: Remove all signal components that exceed the nequest frequency from the signal to be sampled to ensure that the nequest sampling is sufficient to fully record the signal. At the same time, it eliminates all the noise that exceeds the nequest frequency and prevents high-frequency noise from interfering with useful signals.

(3) modulus Conversion

A. Sampling (horizontal discretization)

The sampling time is usually at a fixed interval point. This interval is called a sampling period;

Each point is maintained after sampling ends until the next sampling point. This process is called sampling persistence;

The sampling frequency must be twice the maximum sampling frequency (not equal to)-the phenomenon of mixing;

Sampling takes a limited time, which is called the sampling time of the probe. If the sampling time is not counted, the figure is as follows. If the sampling time is counted, the sampling is maintained. The signal first follows the sampled analog signal for a short time and then reaches the horizontal Persistence State.

 

Sampling is divided into over-sampling and under-sampling. Under-sampling will result in a return to low-frequency signal at a frequency higher than the sampling frequency.

The actual sampling process is as follows:

 

 

B. quantization (discretization of ordinate coordinates ):

Quantitative step size:

 

Quantization Error: quantization value-actual value

Dynamic Range of the quantizer:

 

Quantization scheme: from the minimum value of the simulation range, the quantization level is allocated to the first half interval instead of the first whole interval, then the quantization error is half smaller and half of the quantization step.

The difficulty of signal-to-noise ratio differentiation between signals and noise. The greater the signal-to-noise ratio, the stronger the signal.

 

When the maximum allowable quantization error level is determined, the quantified bits can be calculated:

 

 

 

C. Digital Signal Features of modulus Conversion

The number of allowed digital signals is limited by the number of BITs used by the computer

The digital signal is valid only at the time of sampling and is not defined between sampling points.

(4) digital-to-analog conversion

A. analog conversion level

B. Smooth zero-order Signal

(5) Anti-Image Filter

When the original signal is restored from the sample value, the overlap issue is very important. It can be solved through a low-pass filter, and the low-frequency can pass through, while the high-frequency component is attenuated. The filter can select the spectrum that matches the original spectrum from all the images in the frequency domain.

 

Purpose: filter out unnecessary high-frequency signals, while also filtering out-of-band noise.

 

 

Digital Signal Processing (I)