(New page: ==Question from ECE QE CS Q1 August 2000== ---- ==Share and discuss your solutions below.== ---- =Solution 1 (retrived from [[ECE600_QE_2000_August|her...) |
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==Question from [[ECE_PhD_QE_CNSIP_2000_Problem1|ECE QE CS Q1 August 2000]]== | ==Question from [[ECE_PhD_QE_CNSIP_2000_Problem1|ECE QE CS Q1 August 2000]]== | ||
| − | + | <math class="inline">\mathbf{X}\left(t\right)</math> is a WSS process with its psd zero outside the interval <math class="inline">\left[-\omega_{max},\ \omega_{max}\right]</math> . If <math class="inline">R\left(\tau\right)</math> is the autocorrelation function of <math class="inline">\mathbf{X}\left(t\right)</math> , prove the following: <math class="inline">R\left(0\right)-R\left(\tau\right)\leq\frac{1}{2}\omega_{max}^{2}\tau^{2}R\left(0\right).</math> (Hint: <math class="inline">\left|\sin\theta\right|\leq\left|\theta\right|</math> ). | |
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==Share and discuss your solutions below.== | ==Share and discuss your solutions below.== | ||
Revision as of 08:54, 27 June 2012
Contents
Question from ECE QE CS Q1 August 2000
$ \mathbf{X}\left(t\right) $ is a WSS process with its psd zero outside the interval $ \left[-\omega_{max},\ \omega_{max}\right] $ . If $ R\left(\tau\right) $ is the autocorrelation function of $ \mathbf{X}\left(t\right) $ , prove the following: $ R\left(0\right)-R\left(\tau\right)\leq\frac{1}{2}\omega_{max}^{2}\tau^{2}R\left(0\right). $ (Hint: $ \left|\sin\theta\right|\leq\left|\theta\right| $ ).
Solution 1 (retrived from here)
Solution 2
Write it here.
