# 电气工程代写|信号和系统代写signals and systems代考|ECEN314

## 电气工程代写|信号和系统代写signals and systems代考|Overlap Add Method

Let $N_1$ be the length of longer sequence and $N_2$, the length of smaller sequence. Let the longer sequence be divided into sections of size $N_3$ samples. (Note: Normally the longer sequence is divided into sections of size same as that of smaller sequence.).
The linear convolution of each section with smaller sequence will produce an output sequence of size $N_3+N_2-1$ samples. In this method last $N_2-1$ samples of each output sequence overlaps with the first $N_2-1$ samples of next section. While combining the output sequences of the various sectioned convolutions, the corresponding samples of overlapped regions are added and the samples of nonoverlapped regions are retained as such.

Let $N_1$ be the length of longer sequence and $N_2$, the length of smaller sequence. Let the longer sequence be divided into sections of size $N_3$ samples.

In overlap save method, the result of linear convolution is obtained by circular convolution. Hence, each section of longer sequence and the smaller sequence are converted to the size of the output sequence of size $N_3+N_2-1$ samples. The smaller sequence is converted to size of $N_3+N_2-1$ samples by appending with zeros. The conversion of each section of longer sequence to the size $N_3+N_2-1$ samples can be performed in two different methods.
Method I
In this method the first $N_2-1$ samples of a section are appended as last $N_2-$ 1 samples of the previous section. The circular convolution of each section will produce an output sequence of size $N_3+N_2-1$ samples. In this output the first $N_2-1$ samples are discarded and the remaining samples of the output of sectioned convolution are saved as the overall output sequence.

## 电气工程代写|信号和系统代写signals and systems代考|In-Plane Computation

The flow graph of Fig. $2.63$ describes an algorithm for the computation of the DFT. In the flow graph the branches connecting the nodes and the transmittance of each of these branches. No matter how the nodes in the flow graph are rearranged, it will always represent the same computation provided that the connection between the nodes and the transmittance of the connection are maintained. The particular form for the flow graph in Fig. $2.63$ arose out of deriving the algorithm by separating the original sequences into the even-numbered and odd-numbered points and then continuing to create smaller and smaller subsequences in the same way. An interesting by-product of this derivation is that this flow graph, in addition to describing an efficient procedure for computing the discrete Fourier transform, also suggests a useful way of storing the original data and storing the results of the computation in intermediate arrays.

When implementing the computation depicting in Fig. $2.63$ we can imagine the use of two arrays of (complex) storage registers, one for the arrays being computed and one for the data being used in the computation. For example, in computing the first array in Fig. 2.63, one set of storage registers would contain the input data and the second set would contain the computed results for the first stage. We denote the sequence of complex numbers resulting from the $n$th stage of computation as $X_m(l)$ where $l=0,1, \ldots N-1$, and $m=1,2, \ldots, v\left[v=\log 2^N\right]$. Furthermore, for convenience we define the set of input samples of $X_0[l]$. We can think of $X{m-1}[l]$ as the input array and $X_m(l)$ as the output array for the $m$ th stage computation. Thus, for the case $N=8$ as in Fig. 2.63, we get
$$\begin{array}{ll} X_0[0]=x[0] & X_0[4]=x[1] \ X_0[1]=x[4] & X_0[5]=x[5] \ X_0[2]=x[2] & X_0[6]=x[3] \ X_0[3]=x[6] & X_0[7]=x[7] \end{array}$$
Using this notation, the basic butterfly diagram is drawn as shown in Fig. 2.63. with the associated equation as,
\begin{aligned} X_m[p] &=X_{m-1}[p]+W_N^r X_{m-1}[q] \ X_m[q] &=X_{m-1}[p]-W_N^r X_{m-1}[q] \end{aligned}

# 信号和系统代考

## 电气工程代写|信号和系统代写signals and systems代考|In-Plane Computation

X0[0]=X[0]X0[4]=X[1] X0[1]=X[4]X0[5]=X[5] X0[2]=X[2]X0[6]=X[3] X0[3]=X[6]X0[7]=X[7]

X米[p]=X米−1[p]+在ñrX米−1[q] X米[q]=X米−1[p]−在ñrX米−1[q]

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