UNIT 7 DSP Processor Fundamentals
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New words and Technical Terms
outperform delay discrete time difference digital signal processing (DSP) development time register transfer level (RTL) general purpose microprocessor (GPP) cycles per instruction (CPI)
2
flexibility operand coefficient
latency filter algorithm
Finite impulse response (IIR) infinite impulse response (FIR) analog to digital converter (ADC) digital to analog converter (DAC)
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Text
In the literature, the definition of a digital signal processor takes many forms. In a strict sense, a DSP is any microprocessor that processes digitally represented signals. A DSP filter for example, takes one or more discrete inputs, xi[n], and produces one corresponding output, y[n] for n = …, -1,0, 1, 2, …, and i = 1, …, N, where n is the nth input or output at time n, i is the ith coefficient and N is the length of the filter.
4
In effect, the DSP implements the discrete-time system. As its name implies, it is assumed that there must be some form of preprocessing if the signals are in the continuous time domain, and this is easily accomplished by an analog to digital converter (ADC) [1]. [1].正如它名字所暗示的,连续时域信号必须要 正如它名字所暗示的, 正如它名字所暗示的 经过某种形式的预处理才能被它所处理, 经过某种形式的预处理才能被它所处理,当然这 很容易由模数转换器来完成。 很容易由模数转换器来完成。
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句中its指代 引导的是状语, 句中 指代DSP,as引导的是状语,it is 指代 , 引导的是状语 assumed that there must be some form of preprocessing if the signals are in the continuous time domain中that之后是宾语从 中 之后是宾语从 引导的是条件状语从句。 句,if引导的是条件状语从句。 引导的是条件状语从句 In general, DSP functions are mathematical operations on real-time signals and are repetitive an numerically intensive.
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Samples from real-time signals can number in the millions and hence a large memory bandwidth is needed. processors are created with an architecture unlike those of conventional microprocessors [2]. [2].正是由于这一特性,在发明DSP处理器时采 正是由于这一特性,在发明 正是由于这一特性 处理器时采 用了一种与传统的微处理器不同的结构体系。 用了一种与传统的微处理器不同的结构体系。
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It is
because of this very nature that DSP
此句中的It 是强调句型, 此句中的 is…that是强调句型,这种句型可以 是强调句型 强调句子的主语,宾语,状语等, 强调句子的主语,宾语,状语等,被强调的部分 直接放在be动词之后,本句是强调状语部分, 直接放在 动词之后,本句是强调状语部分, 动词之后 即because of this very nature; unlike those ; of conventional microprocessors则是用于说 则是用于说 明architecture的。 的 Most DSP algorithms are not complicated and only require multiply and accumulate calculations.
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Most, if not all, DSP processors have circuitry built and hard wired to execute these calculations as fast as possible. The signal processing algorithms and functions define a suitable architecture for implementation. We use a simple example of an FIR filter as a basis for the building blocks of the DSP architecture.
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One algorithm used to create an FIR filter uses a direct form on tapped delay line structure with M+1 taps. The M+1 most recent input samples are saved as “filter states”.
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According to Equation (
  1),
y(n) = ∑ci x(n i)
i=0
M
(2-
  1)
the products of each filter state x(n-i) and its corresponding coefficient ci are accumulated or added to produce the current output sample y(n). We can also use the signal flow graph as shown in Fig. 2-1 to represent this algorithm [3].
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[3].我们也可以用图 中的信号流程图来介绍 我们也可以用图2-1中的信号流程图来介绍 我们也可以用图 这个算法。 这个算法。 However it is not clear as to the sequence of the computations since it looks like all the operations can be carried out at the same time. Thus, a more accurate picture has to be formed by using microoperations at the register transfer level (RTL),
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sequenced temporarily from left to right as seen in Fig. 2-
  2.
x(n)
z-1
z-1
z-1
c0
c1
...
c(M-
  1)
cM y(n)
Fig. 2-
  1. Tapped delay line structure of a FIR filter.
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x(n) y(n) D1
Input and Output
D1
D1
Date M emory
T1
T1
T1
T1
T1 Temporary M emory
...
c0 c1 c (M)
time
Arithmetic Operations
Coefficient M emory
Fig. 2-
  2. Register transfer level representation of a FIR filter. 14
The delayed inputs are stored in the data memory, D1 and the coefficients, c0, c1, c(M) are located in the coefficient memory. The contents of both memories are fetched and multiplied together. The result is then added to the temporary memory, T1 is where the results of the previous taps are stored. This cycle is repeated with a different coefficient until completion, producing the final result as y(n). 15
We can make certain assumptions for a fundamental general purpose DSP architecture. From our understanding of DSP algorithms, we see that most computations are multiply and add operations. Looking at the example from the previous section, we will require multiple memory units for storage of different data as well as memory for the arithmetic operation sequences.
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Registers can serve as temporary storage locations and buses will be needed to connect these units together. At this point, the reader may be tempted to ask how this design is different from a general purpose microprocessor (GPP). If we react the issues central to a DSP function, most DSP calculations are repetitive, require a large memory bandwidth and numeric precision, all executed in real time. 17
One might also argue that modern GPPs have clock speeds and cycles per instruction (CPI) that outperform DSP processors but GPPs have operations and program flexibility that are unnecessary for DSP [4]. [4].也许有人认为现代的通用处理器比 也许有人认为现代的通用处理器比DSP有更 也许有人认为现代的通用处理器比 有更 高的处理速度和指令周期, 高的处理速度和指令周期,但是通用处理器有许 不必要的运算和编程的灵活性。 多DSP不必要的运算和编程的灵活性。 不必要的运算和编程的灵活性
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DSPs must execute their tasks efficiently while keeping cost, power consumption, memory usage and development time low, especially in the age of mobile computing. Since many signal processing applications process millions of samples of data for every second of operation, the minimum sample period is usually more important than the computationa latency of the processor. 19
We define the sample period as the time between each sequential sample of the input data. The time difference between the input data and the result of its computation is known as the computational latency. Once the initial sample is calculated with certain latency, the subsequent results will however, be produced at the sample period rate.
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As the number of calculations increases, the relatively larger latency of the processor will be negligible compared to the sample rate.
Exercises: Ⅰ,Ⅱ
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数学公式的表示与读法(Ⅰ) 数学公式的表示与读法(
基本运算符号
A+B = C A-B = C A×B = C × A/B=C A:B
  0.3 % A plus B equals C A minus B equals C A multiplied by B equals C A divided by B equals C The ratio of A to B Zero point three percent x squared
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A : B = C : D A is to B of A to B as C is to D
X
2
X3 X4
X
1 2
x cubed x to the fourth power x to the one-half power
19
e =
  1.6×10
x
3 n
e equals one point multiplied by ten to minus nineteenth power The square root of x The cube of x The nth root of x A equals B A is identical with B; A is equivalent to B
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x x
A=B A≡B
A≠B A≈B A>B A<B A≥B A << B
A is not equal to B A be approximately equal to B A is greater than B A is less than B A is greater than or equal to B A is far less than B
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简单函数
f (x)
Function of x
The function of x equals a f (x) = ax2 + bx + c times the square of x plus b times x plus c |a|=b Max f(x) Min f(x) The absolute value of a equals that of b The maximum value of f(x) The minimum value of f(x) A sub n approaches / tends to infinity. The limit of b
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an →∞
lim b
1 limSn = 3 n→∞
( A+ B)C
x +A 2 2 (x + B)
5
The limit of Sn as n gets arbitrarily large is one third. The quantity A plus B times C x to the fifth power plus A over (divided by) the quantity x squared plus B, to the two-thirds power Log of x Log of x to the base two
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log x
log 2 x
 

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