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Phase of a real number

What is the difference between phase delay and group delay?How do you relate imaginary numbers with phase shift? How to imagine this?Phase factors for an 32 point fftbaffled by fft phase spectrum!How are phase values able to capture motion from video?In filter design, why isn't it possible to have a frequency response with phase 0?Extracting accurate phase and amplitude information from FFT with an arbitrary number of samplesContinuous phase for phase delay calculus in FIR filtersPhase spectrum of 2D real functionPlotting the Phase Response

2

$begingroup$

Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?

I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.

phase

share|improve this question

asked Mar 29 at 21:24

NioushaNiousha

1546

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  do you know about phase unwrapping?
  $endgroup$
  – robert bristow-johnson
  Mar 29 at 21:33
  
  

  
  
  
  

add a comment | 

2

$begingroup$

Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?

I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.

phase

share|improve this question

asked Mar 29 at 21:24

NioushaNiousha

1546

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  do you know about phase unwrapping?
  $endgroup$
  – robert bristow-johnson
  Mar 29 at 21:33
  
  

  
  
  
  

add a comment | 

$begingroup$

Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?

I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.

phase

share|improve this question

asked Mar 29 at 21:24

NioushaNiousha

1546

$endgroup$

share|improve this question

asked Mar 29 at 21:24

NioushaNiousha

1546

share|improve this question

asked Mar 29 at 21:24

NioushaNiousha

1546

asked Mar 29 at 21:24

NioushaNiousha

1546

asked Mar 29 at 21:24

NioushaNiousha

1546

1 Answer
1

active

oldest

votes

4

$begingroup$

Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.

"Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.

Your question is equivalent to "For what values of arg(z) is z a real number?"

If that is meaningless to you, I suggest you start by reading two blog articles of mine:

The Exponential Nature of the Complex Unit Circle

And the newest:

Angle Addition Formulas from Euler's Formula

There are of course many other searches. Your terms should be "complex plane real values" for a start.

This is essential foundation material for a lot of DSP concepts.

share|improve this answer

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

$endgroup$

add a comment | 

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4

$begingroup$

Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.

"Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.

Your question is equivalent to "For what values of arg(z) is z a real number?"

If that is meaningless to you, I suggest you start by reading two blog articles of mine:

The Exponential Nature of the Complex Unit Circle

And the newest:

Angle Addition Formulas from Euler's Formula

There are of course many other searches. Your terms should be "complex plane real values" for a start.

This is essential foundation material for a lot of DSP concepts.

share|improve this answer

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

$endgroup$

add a comment | 

4

$begingroup$

Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.

"Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.

Your question is equivalent to "For what values of arg(z) is z a real number?"

If that is meaningless to you, I suggest you start by reading two blog articles of mine:

The Exponential Nature of the Complex Unit Circle

And the newest:

Angle Addition Formulas from Euler's Formula

There are of course many other searches. Your terms should be "complex plane real values" for a start.

This is essential foundation material for a lot of DSP concepts.

share|improve this answer

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

$endgroup$

add a comment | 

$begingroup$

Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.

"Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.

Your question is equivalent to "For what values of arg(z) is z a real number?"

If that is meaningless to you, I suggest you start by reading two blog articles of mine:

The Exponential Nature of the Complex Unit Circle

And the newest:

Angle Addition Formulas from Euler's Formula

There are of course many other searches. Your terms should be "complex plane real values" for a start.

This is essential foundation material for a lot of DSP concepts.

share|improve this answer

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

$endgroup$

share|improve this answer

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

edited Mar 29 at 22:06

MBaz

9,02041733

edited Mar 29 at 22:06

MBaz

9,02041733

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312

answered Mar 29 at 22:02

Cedron DawgCedron Dawg

3,0982312