With the development of the computer and the development of electronic technology, people have entered the MPC (Multimedia Computer) era, people's life is inseparable from multimedia computers. Below is some of the author's study in multimedia processing, let us take a look at multimedia information. How is it processed by a computer.
To talk to multimedia information, we will start from our real life! Everything in the world is a continuous simulation world in the eyes of people. For example, the acoustic wave collected is a continuous time. We call this signal as an analog signal. Let's take a look at our computer. According to Vonniman principle, it is said that the electronic computer is working in two states in the electronic line, that is, the switching circuit is confusing high, low level, using it to represent 0 and 1 two Digital, use the interview structure, then in our computer is 0 and 1, we have become a digital signal, they are discrete, then there is a problem, the analog signal we collect must pass by A / D (Digital Mode Transformation) can be accepted by our computer, then let's take a look at the A / D conversion.
In theory, we use the Fourier fraction of the calculus to handle digital-to-analog conversion or analog to digital conversion, specific reference signal processing, we only look at the chart, there is an analog signal as shown in the figure,
Figure one
We use a pulse signal to superimpose, as shown in Figure 2
Figure II
Just like our junior high school learning function coordinate drawing, this curve, we can use countless multiple points, the more description points, the more descriptions described, which may be non-periodic. After the sample is sampled three
Figure three
This becomes a digital signal, and the algorithm is used to handle the Fourier fraction.
* References in a paragraph, the material learning [Ji Renxin Zhao Wei Dong Xiaogang "Digital Synthetic Cycle Signal Spectrum and Signal Needs" Journal of Tsinghua University 2000 Vol.40 No.1 P.21-24]
Digital spectrum of non-uniform sample period signals
Set g (t) is an analog signal that converts the spectrum GA (Ω) of analog signals to the analog signal.
. Samples of the signal G (t) are sampled in the following manner, but the interval between adjacent sampling points is equal to the interval between each sampling point, that is, the total sampling period is MT, T is average Sampling cycle, as shown in Figure 3. Figure 3 Non-uniform sampling of the signal
Digital spectrum of non-uniform sampled signals can be expressed as
(1)
The RM = (MT-TM) / T is the ratio of MT-TM and the average sampling period T. Setting F (t) is a signal that period is T0. f (t) is not uniformly sampled in the above manner, and the total sampling period is MT. F (t) Fourier fraction can be expressed as
(2)
Where: angular frequency ω0 = 2π / t0, and the n-order Fourier grade calculation. Fourier transform of f (t)
(3)
According to the determination principle of the frequency band of the cycle signal [3], 2N1 (N1 is an integer) is used as a frequency band of the periodic signal, and the formula (3) can be rewritten as
(4)
From the formula (1) and formula (4)
(5)
FS = 1 / t in the formula is the average sampling frequency. Current definition a (n, k) (- ∞)
< ∞, -∞
< ∞, and K, N is integer)
(6)
The equation (5) can be written as
(7)
The formula (6) and the formula (7) are spectrum expressions for non-uniform sampling period signals. The nature of the non-uniform sample period signal spectrum is: 1) As can be seen from the formula (6), sequence A (n, k) is a periodic function of K, which is M, and therefore, f (ω) in formula (7) It is the cycle function of Ω, the cycle is 2π / t = 2πfs; 2) The periodic signal is not uniformly sampled, and each line of FA (Ω) is produced by "parasitic line"; these "parasite" The line "is uniformly distributed on the frequency axis F, and the adjacent line interval is fs / m. The above properties indicate that the nth-order harmonic component of the non-uniform sampling period signal is located at Nω0 on the frequency axis, and the amplitude is 为 (n, 0) |; and "parasitic line" is located (m = 1, ..., M-1), the magnitude of | a (n, m) |. As can be seen from the formula (6), limited sequence a (n, k) is a sequence discrete Fourier transform, by the Parseval theorem
(8)
Thus, the signal-to-noise ratio of non-uniform sample period signal can be written as
(9) Look at an example, we know that the sampling frequency of CD music is usually 44.1k, which is 44.1k, which is a second, generally returns the sample by 16, and of course there is a higher boutique CD, with 16-bit For example, a second music capacity is 176.4KB, 650M CD can play 61 minutes of music, but it has reached a high sound quality.
When the signal enters the computer, let's take a look at how the digital signal is processed in the computer, for example, a photo of a A4 formation (21.6cm × 30m), if you use 12 points / mm (dpm) The amount of data is 25MB with 24-bit color signal, which is very clear, this is a common Windows bitmap file (.bmp) disadvantage is that the picture is too large. Today, in the network, this format picture is obviously not good on the network, so people have to get a small capacity, clear format, and common image group (.jpg) to analyze BMP pictures, We can draw a small part of it, the rest, the sharpness of this picture is reduced, and the capacity of the picture is greatly reduced. For people's eyes, it will not be bmp picture with JPG picture. Clearness, only when magnifying pictures, in order to separate the quality of the picture, we call the compression of this picture to be ineffective compression. To analyze JPEG technology, the existing JPEG technology uses a discrete cosine transform algorithm (DCT) to compress the image data into a "pixel information module" of the square 8 × 8 in a smooth process and arrange the storage to form compression in a certain order. Document, after multiple compression, the image file only reserves the most important data information, and the naked eye is of course different. There is another way to use the Wavelet transform algorithm, which uses the frequency domain or time domain, that is, in the signal analysis, the high-frequency component is sampled, so that it can be constructed. The high definition of the farm, this algorithm has a great improvement of JPEG compression, but it is still damaged compression. This compression is also applied to video processing.
As a new generation of pictures, JPEG 2000 uses prediction methods as an image to lossless encoding method. Make it to achieve lossless compression or interactive compression (retaining a part of the image low compression ratio to seek clarity). As a representative of lossless compression, let's take a look at the GIF picture format that is often seen in daily life, which is implemented by the LZ algorithm. Take a look at the LZ algorithm, it is a dictionary coding method, which is based on the algorithm published in Lempel and Ziv, which is called the LZ algorithm, which includes; LZSS, LZW, LZ77, etc., are non-destructive algorithms. (Not finished) < ∞, -∞ < ∞, and K, N is integer)
