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Buffer signal vector into matrix of data frames

`y = buffer(x,n)`

y = buffer(x,n,p)

y = buffer(x,n,p,opt)

[y,z] = buffer(...)

[y,z,opt] = buffer(...)

`y = buffer(x,n)`

partitions
a length-`L`

signal vector `x`

into
nonoverlapping data segments (frames) of length `n`

.
Each data frame occupies one column of matrix output `y`

,
which has `n`

rows and `ceil(L/n)`

columns.
If `L`

is not evenly divisible by `n`

,
the last column is zero-padded to length `n`

.

`y = buffer(x,n,p)`

overlaps
or underlaps successive frames in the output matrix by `p`

samples:

For

`0`

<`p`

<`n`

(overlap),`buffer`

repeats the final`p`

samples of each frame at the beginning of the following frame. For example, if`x`

=`1:30`

and`n`

=`7`

, an overlap of`p`

=`3`

looks like this.The first frame starts with

`p`

zeros (the default initial condition), and the number of columns in`y`

is`ceil(L/(n-p))`

.For

`p`

<`0`

(underlap),`buffer`

skips`p`

samples between consecutive frames. For example, if`x`

=`1:30`

and`n`

=`7`

, a buffer with underlap of`p`

=`-3`

looks like this.The number of columns in

`y`

is`ceil(L/(n-p))`

.

`y = buffer(x,n,p,opt)`

specifies
a vector of samples to precede `x(1)`

in an overlapping
buffer, or the number of initial samples to skip in an underlapping
buffer:

For

`0`

<`p`

<`n`

(overlap),`opt`

specifies a length-`p`

vector to insert before`x(1)`

in the buffer. This vector can be considered an*initial condition*, which is needed when the current buffering operation is one in a sequence of consecutive buffering operations. To maintain the desired frame overlap from one buffer to the next,`opt`

should contain the final`p`

samples of the previous buffer in the sequence. See Continuous Buffering below.By default,

`opt`

is`zeros(p,1)`

for an overlapping buffer. Set`opt`

to`'nodelay'`

to skip the initial condition and begin filling the buffer immediately with`x(1)`

. In this case,`L`

must be`length(p)`

or longer. For example, if`x`

=`1:30`

and`n`

=`7`

, a buffer with overlap of`p`

=`3`

looks like this.For

`p`

<`0`

(underlap),`opt`

is an integer value in the range`[0,-p]`

specifying the number of initial input samples,`x(1:opt)`

, to skip before adding samples to the buffer. The first value in the buffer is therefore`x(opt+1)`

. By default,`opt`

is zero for an underlapping buffer.This option is especially useful when the current buffering operation is one in a sequence of consecutive buffering operations. To maintain the desired frame underlap from one buffer to the next,

`opt`

should equal the difference between the total number of points to skip between frames (`p`

) and the number of points that were*available*to be skipped in the previous input to`buffer`

. If the previous input had fewer than`p`

points that could be skipped after filling the final frame of that buffer, the remaining`opt`

points need to be removed from the first frame of the current buffer. See Continuous Buffering for an example of how this works in practice.

`[y,z] = buffer(...)`

partitions
the length-`L`

signal vector `x`

into
frames of length `n`

, and outputs only the *full* frames
in `y`

. If `y`

is an overlapping
buffer, it has `n`

rows and `m`

columns,
where `m = floor(L/(n-p))`

when ```
length(opt)
= p
```

or `m = floor((L-n)/(n-p))+1`

when ```
opt
= 'nodelay'
```

.

If `y`

is an underlapping buffer, it has `n`

rows
and `m`

columns, where ```
m = floor((L-opt)/(n-p))
+ (rem((L-opt),(n-p)) >= n)
```

.

If the number of samples in the input vector (after the appropriate
overlapping or underlapping operations) exceeds the number of places
available in the `n`

-by-`m`

buffer,
the remaining samples in `x`

are output in vector `z`

,
which for an overlapping buffer has length `L - m*(n-p)`

when ```
length(opt)
= p
```

or `L - ((m-1)*(n-p)+n)`

when ```
opt
= 'nodelay'
```

, and for an underlapping buffer has length ```
(L-opt)
- m*(n-p)
```

.

Output `z`

shares the same orientation (row
or column) as `x`

. If there are no remaining samples
in the input after the buffer with the specified overlap or underlap
is filled, `z`

is an empty vector.

`[y,z,opt] = buffer(...)`

returns
the last `p`

samples of a overlapping buffer in output `opt`

.
In an underlapping buffer, `opt`

is the difference
between the total number of points to skip between frames (`-p`

)
and the number of points in `x`

that were *available* to
be skipped after filling the last frame:

For

`0`

<`p`

<`n`

(overlap),`opt`

(as an output) contains the final`p`

samples in the last frame of the buffer. This vector can be used as the*initial condition*for a subsequent buffering operation in a sequence of consecutive buffering operations. This allows the desired frame overlap to be maintained from one buffer to the next. See Continuous Buffering below.For

`p`

<`0`

(underlap),`opt`

(as an output) is the difference between the total number of points to skip between frames (`-p`

) and the number of points in`x`

that were*available*to be skipped after filling the last frame:`opt = m*(n-p) + opt - L`

where`opt`

on the right is the input argument to`buffer`

, and`opt`

on the left is the output argument.`z`

is the empty vector. Here`m`

is the number of columns in the buffer, which is`m = floor((L-opt)/(n-p)) + (rem((L-opt),(n-p))>=n)`

.Note that for an underlapping buffer output

`opt`

is always zero when output`z`

contains data.The

`opt`

output for an underlapping buffer is especially useful when the current buffering operation is one in a sequence of consecutive buffering operations. The`opt`

output from each buffering operation specifies the number of samples that need to be skipped at the start of the next buffering operation to maintain the desired frame underlap from one buffer to the next. If fewer than`p`

points were available to be skipped after filling the final frame of the current buffer, the remaining`opt`

points need to be removed from the first frame of the next buffer.

In a sequence of buffering operations, the `opt`

output
from each operation should be used as the `opt`

input
to the subsequent buffering operation. This ensures that the desired
frame overlap or underlap is maintained from buffer to buffer, as
well as from frame to frame within the same buffer. See Continuous Buffering below for an example
of how this works in practice.

Error messages are displayed when `p`

≥`n`

or `length(opt)`

≠`length(p)`

in
an overlapping buffer case:

Frame overlap P must be less than the buffer size N. Initial conditions must be specified as a length-P vector.

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