# ADDPHASE

## Purpose:

Adds a constant phase value to a series.

## Syntax:

ADDPHASE(series,
p)

series |
- |
A series or array. |

p |
- |
A real, the phase value in radians. |

## Returns:

A series or array.

## Example:

W1: gsin(1000, 1/1000, 3)

W2: gcos(1000, 1/1000, 3)

W3: addphase(w1, pi/2)

W4: w2-w3

W1 contains a 3 Hz
sine wave with a sample rate of 1000 Hz.

W2 contains a 3 Hz
cosine wave with a sample rate of 1000 Hz.

W3 adds *π*/2 radians of phase shift to the
sine wave.

W4 displays the difference
between the cosine and the phase shifted sine.

## Example:

W1: 1..10

W2: -w1

W3: addphase(w1, pi)

W4: w2-w3

W1 contains a linear
ramp.

W2 inverts the ramp.

W3 adds *π* radians of phase shift to the sine
wave.

W4 displays the difference
between the inverted ramp and the
phase shifted ramp.

## Example:

W1: gcos(1000, 1/1000, 3)

W2: gcos(1000, 1/1000, 9)

W3: w1 + w2

W4: addphase(w3, pi/4)

W5: addphase(w1, pi/4) + addphase(w2,
pi/4)

W6: w4 - w5

W1 and W2 each contain
a cosine wave.

W3 sums the cosines.

W4 adds *π*/4 radians of phase shift to the
sum.

W5 adds *π*/4 radians of phase shift to each
component and then
sums.

W6 shows the results
are identical to machine precision.

## Remarks:

ADDPHASE adds a phase constant to the
PHASE of the FFT
of the input series. The result is transformed back to the time domain.

If the series is purely real, the phase
input value is converted to an anti-symmetric constant series and added
to the original phase. The original DC phase value is preserved or set
to *π* if the phase input
is an odd multiple of *π*.
If the
series is real and even length, the original Nyquist phase value is also
preserved or set to -*π*
if the phase input is an odd multiple of phase. This handling of DC and
Nyquist phase inverts the input series for a phase input of +- *Nπ* for *N*
odd.

## See Also:

FFT

MAGNITUDE

PHASE

PHASEDIFF