This article introduced uses in calculating the separate time domain (digit) the sequence derivative highly effective computing network. This article described one simply in view of the recursion derivative network, and may guarantee that linear phase the minute meets the delay line (limited impact on respond, or calls FIR) the differentiator.
In the continuous signal domain, the differential definition is clear, but is not true in the separate territory. However, is good in us may the approximate calculation discrete signal differential. (DSP purification discussing likes using “digital difference” this terminology, we use “differentiator”).
 Separate time domain signal ” > |
Must understand that the differential the concept, may consideration type (1) continual sine wave, its frequency be rad. /s.
This sine wave’s derivative is:
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Therefore, the sine wave derivative is the scope in proportion to primitive x(t) sine wave frequency cosine wave. According to type (2), ideal differentiator frequency amplitude response along with frequency Omega increases, but the straight line increases. Considers this point, to following two ordinary discrete time FIR (non-recursion) the differentiator, one is the first order difference, another is a centered difference. They are estimate the digital x(n) time domain signal sequence derivative the simple arithmetic method.
The first order difference simple arithmetic x(n) signal sampling’s difference, in the time domain the definition is continuously:
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This differentiator frequency amplitude response for like Figure 1 dashed line|Hfd (Omega)|. As the comparison, Figure 1 also showed an ideal differentiator straight line|Hidea (Omega)|= amplitude response curve. In the chart frequency axis including the positive frequency scope 0≤ ω≤π sampling/radian, corresponds the 0~fs/2 cycle the frequency range, fs is the x(n) sampling rate, unit for hertz.
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Type 3 succinct, but the shortcoming is it|Hfd (Omega)|The high frequency noise amplification, often will create to the real signal the disturbance. Therefore, in fact frequently uses the middle difference differentiator. The middle difference differentiator’s time domain expression is:
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Middle difference differentiator frequency amplitude response for Figure 1 line between two points|Hcd (Omega)|. |Hcd (Omega)|The ideal high frequency (noise) weakens is restricted, its linearity operating frequency scope for only from 0 to approximately 0.16 Pi sampling/radian (0.08fs Hz) between. It is a pity, this scope is smaller than the first-order differentiator linearity operating frequency scope.
Above already mentioned that this design guide introduced the one kind of third choice, is a highly effective computation differentiator, it maintained the middle difference differentiator high frequency weaken performance merit, simultaneously expanded its linearity operating frequency scope. This differentiator definition is:
This novel differentiator normalized frequency amplitude response for Figure 1 reality|Hdif (Omega)|Line, its linearity operating frequency scope for from 0~ approximately 0.34π sampling/radian (0.17fs Hz), for middle difference differentiator allowed frequency scope two times.
This differentiator realizes as shown in Figure 2, a detention block contains two units to retard. This differentiator’s folding FIR structure as shown in Figure 3, expressed to each ydif(n) output sampling, must only carry on one time to ride. the ydif(n) differentiator’s true flexibility is its non-unit coefficient (±1/16) is 2 entire several times power. Thus, may arithmetic right lateral 4 carry on time to ride. This kind of binary position right lateral is one kind of linear phase non-multiplier’s differentiator.
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ydif(n) differentiator another important characteristic is its time delay (group delay) is precisely three sampling periods (3/fs), causes its to be possible to use in the popular FM demodulation.
