What is digital signal processing?
The first important question we want to answer is why? Where can we apply this knowledge, and wherein our daily life do we encounter digital signal processing (DSP)?
You don’t have to go far to answer this question, just take your smartphone. This device plays audio and video, processes photos, transmits and receives information over the network, evaluates its own position in space, scans a fingerprint or user profile, and all this is achievable through digital signal processing.
There are many examples from everyday life, modern medical devices cannot do without DSP:
- Smart vehicles process a signal from a variety of sensors and independently assess the traffic situation;
- Radar stations monitor the takeoff and landing of aircraft at airfields;
- Telecommunications and global positioning systems are all based on the DSP algorithm.
- Simply put, Digital Signal Processing today surrounds us everywhere and our comfort and safety depend on it.
For note, the use of a matrix is common in signal processing. Using an online matrix multiplication calculator and determinant calculator you can easily get the calculation done.
Everything is about DSP
What is a signal?
A physical process that carries information. If we receive information from some physical process, then for us it becomes a signal.
Let’s consider some examples:
Graph of temperature changes in the area of the international airport “Logan” for one month. On the first graph, the x-axis is time, the y- axis is degrees, this is a one-dimensional signal or an electrocardiogram record. In the second graph, a one-dimensional signal, the change in voltage across the electrodes over time.
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One-dimensional signals
But signals can change in space. For example, an image. It reflects the change in color and illumination in space. If we are considering a digital image, then it usually consists of pixels.
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pixels in the picture
The brightness value of individual pixels changes in space. Each line of pixels can be viewed as a separate, one-dimensional signal. Here the keyword is to consider how we view or represent the signal is very important. For processing, we use a certain mathematical apparatus. What is the luminance value of a pixel of one line? This is a set of numbers over which you can perform, for example, arithmetic operations, or they can be reflected on the graph by plotting along the x-axis the position of pixels in space.
Adding several rows, we get a matrix, the image is often represented precisely in the form of numerical matrices, and this representation, in fact, a mathematical model of the signal, is what we can operate on.
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numeric matrix image
We present the image in the form of a matrix and we can apply linear algebra, or, for example, we can describe the signal with a formula and determine its value by substituting the parameters at any time. We choose a mathematical description for the physical process under consideration depending on the problem to be solved and on the mathematics available to us.
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Signal processing
Signal processing is the execution of actions on a signal to change its characteristics or obtain information. A similar action was previously carried out without the use of computers and microcircuits.
Consider a typical example of amplifying an analog electrical signal. Analog electrical circuits are made up of transistors, resistors, capacitors, and so on. The picture below shows an amplifying stage, it allows obtaining a signal of greater amplitude from a signal of small amplitude, a change in the characteristics of the signal occurs, that is, it’s processing.
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signal amplification
Phase and frequency detector circuits can help us evaluate the characteristics of an electrical signal, that is, obtain information. Analog circuits operate on continuous signals, while digital devices process discrete counts, zeros, and ones.
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Digital signals
In fact, the value of the input signal also changes here and the microcircuit is a digital amplifier.
But why do we even use digital signals and devices?
Digital signals were first used in communication systems, as they were more resistant to noise and interference, and here you can draw an analogy with the Morse code. You probably remember how in the movies, when the communication system stops working, the hero recalls Morse code and starts pressing tangent, transmitting dots and dashes, such a simple signal arrives in the most difficult conditions.
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morse code
Zeros and ones of a digital signal, the same dots, and dashes. They can encode any information, just like we encode letters in the Morse code.
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Analog signal
An analog signal carries information, for example, in the value of its amplitude, and it is important for us to know the exact value in order to receive a message without errors. A digital signal has only two amplitude values, large or small, one or zero.
Analog and Digital Signal differences
During signal transmission, noise superimposes, and in the case of an analog signal, this noise can greatly distort the amplitude value, while in a digital one, we can still understand where is zero and where is one, and decode the message without errors.
The development of digital communication has led to the development of digital computing technology, and as a result, now we have programmable digital computers that are present in almost every device. But analog processing has not gone anywhere, modern devices also often contain analog circuits along with digital ones.
Digital signal processing is a method of processing signals based on numerical methods using digital computing technology.
The picture below is a generalized diagram of a DSP system. It describes the general case of processing a physical, that is, an analog signal by a digital computer.
At the input and output of the processing system, a continuous analog signal, which passes through a special device, an analog-to-digital converter (ADC), and then, in the form of a sequence of zeros and ones, enters the digital calculator. The output sequence converges back to analog form by a digital-to-analog converter.
