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mm（美女）让我帮她翻，我没时间给她翻
要翻的内容是数字信号和模拟信号处理的一个简单教科书式文章，其实就是费点时间，难度比较低。
我全部水晶就这么多了
你不要用软件翻译或在线翻译，别忘了我也是翻译组的
开工前最好说下，免得2个人同时干，1个不白干了
文章如下：图片格式的公式，图，没贴上来，光翻文字就可以了
Input Signal Conditioning
As shown in Figure 1, the analog signal, , is picked up by an appropriate electronic sensor that converts pressure, temperature, or sound into electrical signals.
For example, a microphone can be used to pick up sound signals. The sensor output, , is amplified by an amplifier with gain value g. The amplified signal is
(1)
The gain value g is determined such that has a dynamic range that matches the ADC. For example, if the peak-to-peak range of the ADC is volts (V), then g may be set so that the amplitude of signal to the ADC is scaled between V. In practice, it is very difficult to set an appropriate fixed gain because the level of may be unknown and changing with time, especially for signals with a larger dynamic range such as speech. Therefore an automatic gain controller (AGC) with time-varying gain determined by DSP hardware can be used to effectively solve this problem.
A/D Conversion
As shown in Figure 1, the ADC converts the analog signal into the digital signal sequence . Analog-to-digital conversion, commonly referred as digitization, consists of the sampling and quantization processes as illustrated in Figure 2. The sampling process depicts a continuously varying analog signal as a sequence of values. The basic sampling function can be done with a ‘sample and hold’ circuit, which maintains the sampled level until the next sample is taken. Quantization process approximates a waveform by assigning an actual number for each sample. Therefore an ADC consists of two functional blocks -- an ideal sampler (sample and hold) and a quantizer (includ¬ing an encoder). Analog-to-digital conversion carries out the following steps:
1. The band limited signal is sampled at uniformly spaced instants of time, , where n is a positive integer, and T is the sampling period in seconds. This sampling process converts an analog signal into a discrete-time signal, , with continuous amplitude value.
2. The amplitude of each discrete-time sample is quantized into one of the levels, where B is the number of bits the ADC has to represent for each sample. The discrete amplitude levels are represented (or encoded) into distinct binary words with a fixed wordlength B. This binary sequence, , is the digital signal for DSP hardware.
The reason for making this distinction is that each process introduces different distor¬tions. The sampling process brings in aliasing or folding distortions, while the encoding process results in quantization noise.
Figure 2 Block diagram of A/D converter
Sampling
An ideal sampler can be considered as a switch that is periodically open and closed every seconds and
(2)
where is the sampling frequency (or sampling rate) in hertz (Hz, or cycles per second). The intermediate signal, , is a discrete-time signal with a continuous-value (a number has infinite precision) at discrete time as illustrated in Figure 3. The signal is an impulse train with values equal to the amplitude of at time . The analog input signal is continuous in both time and amplitude. The sampled signal is continuous in amplitude, but it is defined only at discrete points in time. Thus the signal is zero except at the sampling instants .
In order to represent an analog signal by a discrete-time signal accurately, two conditions must be met:
1. The analog signal, , must be bandlimited by the bandwidth of the signal .
2. The sampling frequency, , must be at least twice the maximum frequency com¬ponent in the analog signal . That is,
(3)
This is Shannon's sampling theorem. It states that when the sampling frequency is greater than twice the highest frequency component contained in the analog signal, the original signal can be perfectly reconstructed from the discrete-time sample . The sampling theorem provides a basis for relating a continuous-time signal with the discrete-time signal obtained from the values of taken seconds apart. It also provides the underlying theory for relating operations performed on the sequence to equivalent operations on the signal directly.
Figure 3 Example of analog signal and discrete-time signal .
The minimum sampling frequency is the Nyquist rate, while is the Nyquist frequency (or folding frequency). The frequency interval is called the Nyquist interval. When an analog signal is sampled at sampling frequency, , frequency components higher than fold back into the frequency range . This undesired effect is known as aliasing. That is, when a signal is sampled perversely to the sampling theorem, image frequencies are folded back into the desired frequency band. Therefore the original analog signal cannot be recovered from the sampled data. This undesired distortion could be clearly explained in the frequency domain. Another potential degradation is due to timing jitters on the sampling pulses for the ADC. This can be negligible if a higher precision clock is used.
For most practical applications, the incoming analog signal may not be band-limited. Thus the signal has significant energies outside the highest frequency of interest, and may contain noise with a wide bandwidth. In other cases, the sampling rate may be pre-determined for a given application. For example, most voice commu¬nication systems use an 8 kHz (kilohertz) sampling rate. Unfortunately, the maximum frequency component in a speech signal is much higher than 4 kHz. Out-of-band signal components at the input of an ADC can become in-band signals after conversion because of the folding over of the spectrum of signals and distortions in the discrete domain. To guarantee that the sampling theorem defined in Equation (3) can be fulfilled, an anti-aliasing filter is used to band-limit the input signal. The anti-aliasing filter is an analog lowpass filter with the cut-off frequency of
. (4)
Ideally, an anti-aliasing filter should remove all frequency components above the Nyquist frequency. In many practical systems, a bandpass filter is preferred in order to prevent undesired DC offset, 60 Hz hum, or other low frequency noises. For example, a bandpass filter with passband from 300 Hz to 3200 Hz is used in most telecommunica¬tion systems.
Since anti-aliasing filters used in real applications are not ideal filters, they cannot completely remove all frequency components outside the Nyquist interval. Any fre¬quency components and noises beyond half of the sampling rate will alias into the desired band. In addition, since the phase response of the filter may not be linear, the components of the desired signal will be shifted in phase by amounts not proportional to their frequencies. In general, the steeper the roll-off, the worse the phase distortion introduced by a filter. To accommodate practical specifications for anti-aliasing filters, the sampling rate must be higher than the minimum Nyquist rate. This technique is known as oversampling. When a higher sampling rate is used, a simple low-cost anti-aliasing filter with minimum phase distortion can be used.
Quantizing and Encoding
In the previous sections, we assumed that the sample values are represented exactly with infinite precision. An obvious constraint of physically realizable digital systems is that sample values can only be represented by a finite number of bits. The fundamental distinction between discrete-time signal processing and DSP is the wordlength. The former assumes that discrete-time signal values have infinite wordlength, while the latter assumes that digital signal values only have a limited B-bit.
[ 本帖最后由 大岛老师 于 2008-4-28 10:21 编辑 ] |
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发表于 2008-4-26 12:10
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发表于 2008-4-26 14:11
lz是不会把答案给我的
