Adaptive Filter | ADPCM | ADSP | ADSP-2181 | Aliasing | AMR | Anti-Aliasing | ARMA | Autocorrelation | AutoCovariance | Beamforming | Bessel | Blackfin | Butterworth | C6713 | CCS | Chebyshev | CIC Filter | Circular Convolution | Code Composer Studio | Comb Filter | Compression | Convolution | Cross Correlation | DCT | Decimation | Deconvolution | Demodulation | DM642 | DSP Boards | DSP/BIOS | DTMF | Echo Cancellation | Equalization | Equalizer | ETSI | EZLITE (Ez-kit Lite) | FFT | FFTW | FIR Filter | Fixed Point | FSK | G.711 | G.723 | G.729 | Gaussian Noise | Goertzel | GPIO | Hilbert Transform | IFFT | IIR Filter | Interpolation | Invariance | JTAG | Kalman | Laplace Transform | Levinson | LPC | McBSP | MIPS | Modulation | MPEG | Multirate | Notch Filter | Nyquist | OFDM | Oversampling | Pink Noise | Pitch | PLL | Polyphase | QAM | QDMA | Quantization | Quantizer | Radar | Random Noise | Reed Solomon | Remez | Resampling | RTDX | Sampling | Sharc | TI C6711 | Undersampling | Viterbi | Wavelets | White Noise | Wiener Filter | Windowing | XDS510PP | Z Transform

Hello,
                I am facing problem in finding the pdf of  Z= AB+CD,
where A, B, C, D are  independent normal random variables  with zero
mean and uneqaul variances.
I could bale to find out the pdf's of each term (i.e. AB or CD).  It is
a well known result that AB has a pdf of   modified Bessel function of
the second kind.
 If we add two random variables having the pdf of " modified Bessel
function of the second kind.", assuming both are independent, I am
unable to get the final expression . Since it involves the convolution
of two " modified Bessel function of the second kind.".
Is there any standard expression for finding the pdf of
z= AB+CD?
Best Regards,
-SaiRamesh.

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

s...@gmail.com wrote:
> Hello,
>                 I am facing problem in finding the pdf of  Z= AB+CD,
> where A, B, C, D are  independent normal random variables  with zero
> mean and uneqaul variances.
> I could bale to find out the pdf's of each term (i.e. AB or CD).  It is
> a well known result that AB has a pdf of   modified Bessel function of
> the second kind.
>  If we add two random variables having the pdf of " modified Bessel
> function of the second kind.", assuming both are independent, I am
> unable to get the final expression . Since it involves the convolution
> of two " modified Bessel function of the second kind.".
> Is there any standard expression for finding the pdf of
> z= AB+CD?
> Best Regards,
> -SaiRamesh.


I think you can numerically obtain the pdf of z (by plotting in matlab)
 but I do not think any analytical result can be obtained by convolving
2 Bessel functions

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.