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# Spectrum
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A comprehensive Python library for spectral analysis providing various methods for power spectral density (PSD) estimation, parametric spectral analysis, and signal processing utilities. The package includes 174+ functions and 35+ classes across 24+ modules, covering parametric methods, eigenvalue-based methods, non-parametric methods, and extensive signal processing tools.
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## Package Information
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- **Package Name**: spectrum
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- **Package Type**: pypi
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- **Language**: Python
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- **Installation**: `pip install spectrum`
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## Core Imports
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```python
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import spectrum
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```
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Common patterns for specific functionality:
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```python
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from spectrum import *
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# or
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from spectrum import pburg, pyule, pmusic, speriodogram
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```
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## Basic Usage
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```python
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import spectrum
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import numpy as np
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# Generate test signal
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N = 1024
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noise = np.random.randn(N)
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signal = np.sin(2 * np.pi * 0.1 * np.arange(N)) + 0.1 * noise
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# Parametric PSD estimation using Burg method
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p = spectrum.pburg(signal, order=15)
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p.plot()
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# Non-parametric PSD estimation using periodogram
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psd = spectrum.speriodogram(signal, NFFT=512)
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# Eigenvalue-based method (MUSIC)
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music = spectrum.pmusic(signal, IP=15, NSIG=2)
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music.plot()
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# Auto-regressive parameter estimation
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ar_params, noise_var, _ = spectrum.aryule(signal, order=10)
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# Window function generation
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window = spectrum.create_window(64, 'hamming')
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```
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## Architecture
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The spectrum package follows a modular design with several key architectural patterns:
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- **Parametric Spectrum Classes**: Inherit from `ParametricSpectrum` for AR, ARMA, and eigenvalue methods
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- **Fourier Spectrum Classes**: Inherit from `FourierSpectrum` for periodogram and correlogram methods  
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- **Base Spectrum Class**: Common functionality including plotting, scaling, and frequency range handling
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- **Estimation Functions**: Standalone functions for parameter estimation (AR coefficients, reflection coefficients)
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- **Utility Modules**: Signal processing tools, window functions, linear algebra utilities
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This design provides consistent interfaces across different estimation methods while maintaining flexibility for specialized applications in spectral analysis, system identification, and digital signal processing.
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## Capabilities
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### Parametric AR Methods
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Auto-regressive parameter estimation and PSD computation using various algorithms including Yule-Walker, Burg, covariance, and modified covariance methods.
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```python { .api }
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def aryule(X, order, norm='biased', allow_singularity=True): ...
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def arburg(X, order, criteria=None): ...
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def arcovar(x, order): ...
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def modcovar(x, order): ...
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class pyule(data, order, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pburg(data, order, criteria=None, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pcovar(data, order, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pmodcovar(data, order, NFFT=None, sampling=1., scale_by_freq=False): ...
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```
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[Parametric AR Methods](./parametric-ar.md)
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### ARMA Methods
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Auto-regressive moving average parameter estimation and PSD computation for combined AR-MA models and pure MA models.
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```python { .api }
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def arma_estimate(X, P, Q, lag): ...
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def ma(X, Q, M): ...
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def arma2psd(A=None, B=None, rho=1., T=1., NFFT=4096, sides='default', norm=False): ...
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class parma(data, P, Q, lag, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pma(data, Q, M, NFFT=None, sampling=1., scale_by_freq=False): ...
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```
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[ARMA Methods](./arma-methods.md)
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### Eigenvalue Methods
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High-resolution spectral estimation using eigenvalue decomposition including MUSIC, eigenvector, and minimum variance methods.
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```python { .api }
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def music(X, IP, NSIG=None, NFFT=4096, threshold=None, criteria='aic', verbose=False): ...
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def ev(X, IP, NSIG=None, NFFT=4096, threshold=None, criteria='aic', verbose=False): ...
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def minvar(X, order, sampling=1., NFFT=4096): ...
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class pmusic(data, IP, NSIG=None, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pev(data, IP, NSIG=None, NFFT=None, sampling=1., scale_by_freq=False): ...
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class pminvar(data, order, NFFT=None, sampling=1., scale_by_freq=False): ...
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```
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[Eigenvalue Methods](./eigenvalue-methods.md)
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### Non-parametric Methods
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Classical spectral estimation techniques including periodogram, Welch's method, correlogram, and multi-taper methods.
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```python { .api }
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def speriodogram(x, NFFT=None, detrend=True, sampling=1., scale_by_freq=True, window='hamming', axis=0): ...
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def WelchPeriodogram(data, NFFT=None, sampling=1., **kargs): ...
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def pmtm(x, NW=None, k=None, NFFT=None, e=None, v=None, method="adapt", show=False): ...
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class Periodogram(data, sampling=1., NFFT=None, window='hamming', detrend='mean', scale_by_freq=True): ...
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class pcorrelogram(data, sampling=1., lag=-1, window='hamming', NFFT=None, scale_by_freq=True, detrend=None): ...
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class MultiTapering(Spectrum): ...
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```
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[Non-parametric Methods](./nonparametric-methods.md)
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### Linear Prediction and Conversion
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Linear prediction analysis and conversion between different parameter representations (AR coefficients, reflection coefficients, line spectral frequencies).
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```python { .api }
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def LEVINSON(r, order=None, allow_singularity=False): ...
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def lpc(x, N=None): ...
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def ac2poly(data): ...
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def poly2ac(poly, efinal): ...
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def rc2poly(kr, r0=None): ...
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```
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[Linear Prediction](./linear-prediction.md)
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### Window Functions
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Comprehensive collection of window functions for signal processing applications with visualization and analysis tools.
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```python { .api }
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def create_window(N, name=None, **kargs): ...
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def enbw(data): ...
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class Window(N, name=None, **kargs): ...
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def window_hamming(N): ...
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def window_hanning(N): ...
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def window_kaiser(N, beta=8.6): ...
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def window_blackman(N, alpha=0.16): ...
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def window_gaussian(N, alpha=2.5): ...
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```
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[Window Functions](./window-functions.md)
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### Correlation and Signal Processing
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Correlation analysis, signal generation, and essential signal processing utilities for spectral analysis applications.
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```python { .api }
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def CORRELATION(x, y=None, maxlags=None, norm='unbiased'): ...
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def xcorr(x, y=None, maxlags=None, norm='biased'): ...
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def chirp(t, f0=0., t1=1., f1=100., form='linear', phase=0): ...
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def morlet(lb, ub, n): ...
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def pow2db(x): ...
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def db2pow(xdb): ...
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def nextpow2(x): ...
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```
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[Correlation and Signal Processing](./correlation-signal.md)
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### Mathematical Tools and Utilities
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Linear algebra utilities, model selection criteria, transfer function analysis, and mathematical tools supporting spectral analysis.
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```python { .api }
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def CHOLESKY(A, B, method='scipy'): ...
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def pascal(n): ...
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def corrmtx(x_input, m, method='autocorrelation'): ...
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def AIC(N, rho, k): ...
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def MDL(N, rho, k): ...
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def FPE(N, rho, k=None): ...
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class Criteria(name, N): ...
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def tf2zp(b, a): ...
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def zp2tf(z, p, k): ...
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```
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[Mathematical Tools](./math-tools.md)