added complex operations overview

Author: vlazzarini

docs/math/complex.md

@@ -0,0 +1,27 @@
+# **Complex Arithmetic and Operators**
+
+Csound supports all arithmetic and a set of operators for Complex variables
+and arrays:
+
+* +,-, * and / for Complex-Complex, Complex-k, and Complex-i expressions (returning Complex)
+* +,-, * and / for Complex[]-Complex[] and Complex[]-k expressions (returning Complex)
+
+For Complex and Complex[] types, the following functions are supported
+
+* [abs](../opcodes/abs.md) -  magnitude
+* [arg](../opcodes/arg.md) - argument 
+* [complex](../opcodes/complex.md) - rectangular conversion 
+* [conj](../opcodes/conj.md) - conjugation
+* [imag](../opcodes/imag.md) - imaginary part
+* [polar](../opcodes/polar.md) - polar conversion
+* [real](../opcodes/real.md) - real part
+
+Assignment and initialisation are also supported with comma-separated arguments for
+both real and imaginary parts respectively, 
+
+``` csound-orc
+var:Complex = real:{k,i}, imag:{k,i}
+```
+
+
+

docs/math/linearalgebra.md

@@ -5,7 +5,7 @@ category:
 # Linear Algebra Opcodes
 Scalar, vector, and matrix arithmetic on real and complex values.
 
-Plugin opcodes in linear_algebra. This opcode is part of the plugin repository and has to be installed separately. The plugin repository can be found here: [https://github.com/csound/plugins](https://github.com/csound/plugins)
+Plugin opcodes in linear_algebra. These opcodes are part of the plugin repository and has to be installed separately. The plugin repository can be found here: [https://github.com/csound/plugins](https://github.com/csound/plugins)
 
 These opcodes implement many linear algebra operations, from scalar, vector, and matrix arithmetic up to and including QR based eigenvalue decompositions. The opcodes are designed for digital signal processing, and of course other mathematical operations, in the Csound orchestra language.
 

docs/math/mathfunc.md

@@ -5,6 +5,7 @@ Opcodes that perform mathematical functions are:
 * [abs](../opcodes/abs.md)
 * [arg](../opcodes/arg.md)
 * [ceil](../opcodes/ceil.md)
+* [chebyshevpoly](../opcodes/chebyshevpoly.md)
 * [complex](../opcodes/complex.md)
 * [conj](../opcodes/conj.md)
 * [exp](../opcodes/exp.md)
@@ -17,6 +18,7 @@ Opcodes that perform mathematical functions are:
 * [log10](../opcodes/log10.md)
 * [logbtwo](../opcodes/logbtwo.md)
 * [polar](../opcodes/polar.md)
+* [polynomial](../opcodes/polynomial.md)
 * [pow](../opcodes/pow.md)
 * [powershape](../opcodes/powershape.md)
 * [powoftwo](../opcodes/powoftwo.md)
@@ -25,3 +27,5 @@ Opcodes that perform mathematical functions are:
 * [real](../opcodes/real.md)
 * [round](../opcodes/round.md)
 * [sqrt](../opcodes/sqrt.md)
+* [taninv2](../opcodes/taninv2.md)
+

docs/math/opeqfunc.md

@@ -1,13 +1,12 @@
-# **Opcode Equivalents of Functions**
+# **Opcode Equivalents of Arithmetic Operations**
 
-Opcodes that perform the equivalent of mathematical functions are:
+Opcodes that perform the equivalent of arithmetic operations are:
 
-* [chebyshevpoly](../opcodes/chebyshevpoly.md)
 * [divz](../opcodes/divz.md)
 * [mac](../opcodes/mac.md)
 * [maca](../opcodes/maca.md)
-* [polynomial](../opcodes/polynomial.md)
 * [pow](../opcodes/pow.md)
 * [product](../opcodes/product.md)
 * [sum](../opcodes/sum.md)
-* [taninv2](../opcodes/taninv2.md)
+
+

docs/spectral/realtime.md

@@ -87,3 +87,11 @@ A number of opcodes are designed to generate and process streaming partials trac
  [tabifd](../opcodes/tabifd.md)    
 
 See the [Stacks section](../control/stacks.md) for information on the stack opcodes which can stack f-signals.
+
+The following opcodes implement streaming phase vocoder analysis/synthesis for direct pitch and
+timescaling:
+
+* [filescal](../opcodes/filescal.md)
+* [mincer](../opcodes/mincer.md)
+* [mp3scal](../opcodes/mp3scal.md)
+* [temposcal](../opcodes/temposcal.md)

docs/spectral/stft.md

@@ -1,16 +1,15 @@
-# **Short-time Fourier Transform (STFT) Resynthesis**
+# **Phase Vocoder**
 
 > :memo: **Use of PVOC-EX files with the old Csound pvoc opcodes**
 > All the original pvoc opcodes can now read a PVOC-EX file, as well as the native non-portable file format. As the PVOC-EX file uses a double-size analysis window, users may find that this gives a useful improvement in quality, for some sounds and processes, despite the fact that the resynthesis does not use the same window size.
 >
 > Apart from the window size parameter, the main difference between the original .pv format and PVOC-EX is in the amplitude range of analysis frames. While rescaling is applied, so that no significant difference in output level is experienced, whichever file format is used, some slight loss of amplitude can still arise, as the double window usage itself modifies frame amplitudes, of which the resynthesis code is unaware. Note that all the original pvoc opcodes expect a mono analysis file, and multi-channel PVOC-EX files will accordingly be rejected.
 
-Opcodes the implement STFT resynthesis are:
+These are the original phase vocoder resynthesis opcodes in
+Csound. They have been superseeded by [streaming spectral
+analysis](../spectral/realtime.md), which is both more efficient
+and more flexible to use.
 
-* [filescal](../opcodes/filescal.md)
-* [mincer](../opcodes/mincer.md)
-* [mp3scal](../opcodes/mp3scal.md)
-* [temposcal](../opcodes/temposcal.md)
 * [pvadd](../opcodes/pvadd.md)
 * [pvbufread](../opcodes/pvbufread.md)
 * [pvcross](../opcodes/pvcross.md)

mkdocs.yml

@@ -158,6 +158,7 @@ nav:
       - Amplitude Converters: 'math/amp.md'
       - Arithmetic and Logic Operations: 'math/artlogic.md'
       - Comparators and Accumulators: 'sigmod/compaccum.md'
+      - Complex number Operations: 'math/complex.md'
       - Mathematical Functions: 'math/mathfunc.md'
       - Opcode Equivalents of Functions: 'math/opeqfunc.md'
       - Random Functions: 'math/rndfunc.md'
@@ -180,12 +181,12 @@ nav:
       - Slider Banks: 'midi/sliderbk.md'
     - Spectral processing:
       - 'spectral/top.md'
-      - Short-time Fourier Transform (STFT) Resynthesis: 'spectral/stft.md'
-      - Linear Predictive Coding (LPC) Resynthesis: 'spectral/lpcresyn.md'
-      - Non-standard Spectral Processing: 'spectral/nonstand.md'
-      - Tools for Real-time Spectral Processing (pvs opcodes): 'spectral/realtime.md'
+      - Streaming Spectral Processing: 'spectral/realtime.md'
+      - Linear Predictive Coding (LPC): 'spectral/lpcresyn.md'
+      - Phase Vocoder Resynthesis: 'spectral/stft.md'
       - ATS Spectral Processing: 'spectral/ATS.md'
       - Array-based spectral opcodes: 'spectral/arrays.md'
+      - Non-standard Spectral Processing: 'spectral/nonstand.md'
     - Strings:
       - 'strings/top.md'
       - String Manipulation Opcodes: 'strings/manipulate.md'