Lab errata corrected

Author: stiber

Matlab Labs/Lab Book.pdf

@@ -115,7 +115,7 @@
 
 \mbox{}\hfill
 \parbox{1.5in}{\mbox{}}
-\parbox{3in}{Fall 2015}\\[0.25in]
+\parbox{3in}{Fall 2016}\\[0.25in]
 \mbox{}\hfill
 \parbox{3in}{\raggedright
 Michael Stiber\\
@@ -133,7 +133,7 @@
 \newpage
 \mbox{}\vspace{4in}
 \begin{flushright}
-Copyright \copyright\ 2002--2015 by Michael and Bilin Stiber and Eric
+Copyright \copyright\ 2002--2016 by Michael and Bilin Stiber and Eric
 C. Larson\\[2in]
 This work is licensed under the Creative Commons
 Attribution-ShareAlike 4.0 International License. To view a copy of

Matlab Labs/Lab Book.tex

@@ -253,7 +253,7 @@ \subsection{Trigonometric Functions and Complex Mathematics in Matlab}
 \paragraph{Step 2.1} In this step, you are asked to complete a Matlab
 function to synthesize a waveform in the form of:
 \begin{equation*}
-x(t) = \sum_{k=1}^N a_i\cos(2\pi f t + \phi_k)
+x(t) = \sum_{k=1}^N a_k\cos(2\pi f t + \phi_k)
 \end{equation*}
 This is a sum of cosines, all at the same frequency but with different
 phases and amplitudes.  Use the following function prototype to start you off:

Matlab Labs/lab1/lab1.tex

@@ -20,21 +20,15 @@ \subsection{Sampling}
 % where  obj = AnalogSignal
 %        h = hold time in sec (sampling interval)
 %        x = resultant sampled AnalogSignal
-%
-% This function produces a 1D line plot of the provided discrete or digital
-% signal in a "stairstep" fashion. In other words, each value in x (which
-% is a y coordinate of the plotted point (n, x)) is connected by a straight
-% line to the same y value at the next sample number (n+1, x), and then by
-% a vertical line to the next sample value, (n+1, x+1).
 \end{lstlisting}
 
-\paragraph{Step 2.1} Create an analog sine waveform ranging from -5 to
+\paragraph{Step 1.1} Create an analog sine waveform ranging from -5 to
 5V with a frequency of 200Hz and a duration of 2 seconds. Produce a
 plot with X-axis limits set to make the waveform visible (i.e., don't
 just make a 2s plot that tries (and fails) to show 400 cycles of the
 sinusoid.
 
-\paragraph{Step 2.2} Use the \texttt{samplehold} method to produce
+\paragraph{Step 1.2} Use the \texttt{samplehold} method to produce
 sampled versions of this signal at 300Hz, 500Hz, 1000Hz, and
 2000Hz. Use the Matlab \texttt{subplot} command, and the
 \texttt{discreteplot} function provided with this class's Matlab code,
@@ -46,11 +40,11 @@ \subsection{Sampling}
 why not (in other words, your answer to this question should not be
 just ``yes'' or ``no'')?
 
-\paragraph{Step 2.3} Let's look at aliasing in a little more detail
+\paragraph{Step 1.3} Let's look at aliasing in a little more detail
 and with a lot more numerical precision. You'll recall from the text
 that, once we sample a signal, we have limited the range of
 frequencies that we can represent in our discrete signal to the range
-$0 \leq \hat{\omega} \leq \pi/2$, corresponding to a range of apparent
+$0 \leq \hat{\omega} \leq \pi$, corresponding to a range of apparent
 frequencies in the physical world of $0 \leq \omega' \leq \omega_s/2$
 (or $0 \leq f' \leq f_s/2$). Any frequency in the original signal
 above $f_s/2$ will be \emph{aliased} into the range of possible
@@ -60,18 +54,18 @@ \subsection{Sampling}
 plotted. Set up a figure that can hold three plots and plot this
 analog signal in the top plot.
 
-\paragraph{Step 2.4} Sample this signal at 25Hz and use the
+\paragraph{Step 1.4} Sample this signal at 25Hz and use the
 \texttt{discreteplot} function to plot the sampled signal in the
 middle. Sample it at 15Hz and similarly plot that sampled signal at
 the bottom.
 
-\paragraph{Step 2.5} Before examining the plots in detail, answer the
+\paragraph{Step 1.5} Before examining the plots in detail, answer the
 following questions: For each of the two sampling frequencies, what is
 the range of apparent frequencies that can be represented? For each,
 will a sinusoid with $f = 10$Hz be aliased? If so, what will be the
 digital frequency and the apparent frequency of a 10Hz sinusoid?
 
-\paragraph{Step 2.6} Examine the plots and count the number of
+\paragraph{Step 1.6} Examine the plots and count the number of
 up-and-down cycles in each. Don't worry that each cycle doesn't look
 the same, or that every other cycle seems different; just count
 each. You should see 10 cycles in the top graph; how many do you see
@@ -98,7 +92,7 @@ \subsection{Analog to Digital Conversion}
 %      otherwise, set ouput value range = input value range
 \end{lstlisting}
 
-\paragraph{Step 3.1} Write a Matlab function that compares two signals
+\paragraph{Step 2.1} Write a Matlab function that compares two signals
 by computing the \emph{signal to noise ratio} (SNR) that results from
 changing one into the other (by quantization). Your function should do
 this by first computing \emph{root mean squared} (RMS) error between
@@ -121,19 +115,19 @@ \subsection{Analog to Digital Conversion}
 
 
 
-  \paragraph{Step 3.2} Use your code to compute the SNR for a
+  \paragraph{Step 2.2} Use your code to compute the SNR for a
   quantized sinusoid. Generate an analog signal with with a range of 0
   to 5, frequency of 10Hz, and duration 2sec. Sample it at 25Hz. Use
   2, 4, 8, 12, and 16 bits quantization, and plot SNR on the Y-axis
   versus number of quantization bits on the X-axis.
 
-  \paragraph{Step 3.3} Repeat Step 3.2 using a square waveform with
+  \paragraph{Step 2.3} Repeat Step 3.2 using a square waveform with
   the same parameters.
 
-  \paragraph{Step 3.4} Repeat Step 3.2 using a triangle waveform with
+  \paragraph{Step 2.4} Repeat Step 3.2 using a triangle waveform with
   the same parameters.
 
-  \paragraph{Step 3.5} As you double the number of bits used in
+  \paragraph{Step 2.5} As you double the number of bits used in
   quantization, how does the SNR change? How does this compare to what
   your learned from the textbook? Refer to specific features of your
   plots from Steps~3.2--3.4 to justify your answer.

Matlab Labs/lab3/lab3.tex

@@ -189,7 +189,7 @@ \subsection{Frequency Response and Pole-Zero Plots}
 \item Find and sketch the zero locations using pencil and paper, then
   use Matlab to verify this.
 
-\item From the plot of pole locations, sketch the magnitude of the
+\item From the plot of zero locations, sketch the magnitude of the
   frequency response as a function of $\hat{\omega}$ by hand and
   verify this using Matlab. How does the minimum of the magnitude of
   the frequency response relate to the polar representation of the
@@ -303,20 +303,21 @@ \subsection{Linearity and Cascading Filters}
 \paragraph{Step 2.1} A system is called \emph{linear} if a sum of
 different inputs produces an output that is the sum of the outputs for
 the inputs taken individually.  Perform a simple test of the linearity
-of this filter by doubling the input amplitude in Matlab ($X' = 2X = X
-+ X$). How does the new output amplitude compare to the old one?
-
-
-\paragraph{Step 2.2} In one of the self-test exercises in the class
-notes, two filters with transfer functions $H_1(z) = b_0 + b_1z^{-1}$
-and $H_2(z) = b'_0 + b'_1z^{-1}$ were connected in series, and it was
-shown that they could be connected in either order to produce the same
-composite effect (the same overall transfer function). Redo this
-exercise using the \emph{defining equations} for the two filters,
-i.e., $y_1[n] = F_1(x[n])$ for the filter with transfer function
-$H_1(z)$ and $y_2[n] = F_2(x[n])$ for the filter with transfer
-function $H_2(z)$. In other words, show that $F_2(F_1(x[n])) =
-F_1(F_2(x[n]))$.
+of the filter from step 1.2 by doubling the input amplitude in Matlab
+($X' = 2X = X + X$). How does the new output amplitude compare to the
+old one?
+
+
+\paragraph{Step 2.2} In one of the self-test exercises in the
+textbook, two filters with transfer functions $H_1(z) = b_0 +
+b_1z^{-1}$ and $H_2(z) = b'_0 + b'_1z^{-1}$ were connected in series,
+and it was shown that they could be connected in either order to
+produce the same composite effect (the same overall transfer
+function). Redo this exercise using the \emph{defining equations} for
+the two filters, i.e., $y_1[n] = F_1(x[n])$ for the filter with
+transfer function $H_1(z)$ and $y_2[n] = F_2(x[n])$ for the filter
+with transfer function $H_2(z)$. In other words, show that
+$F_2(F_1(x[n])) = F_1(F_2(x[n]))$.
 
 
 \paragraph{Step 2.3} Use Matlab to implement a 50\% duty cycle square

Matlab Labs/lab4/lab4.tex

@@ -99,7 +99,7 @@ \subsection{Impulse Response}
 
 
 \paragraph{Step 2.3} The impulse response of a filter is $h[n]
-        = x[n] + 2x[n-1] + x[n-2] - x[n-3]$, or equivalently,
+        = \delta[n] + 2\delta[n-1] + \delta[n-2] - \delta[n-3]$, or equivalently,
         $h[n]=\{1,2,1,-1\}$, $n=\{0, 1, 2, 3\}$. Determine the
         response of the system to the input signal $x[n]=\{1,2,3,1\}$,
         $n=\{0, 1,2,3\}$ by hand. Use Matlab to check your
@@ -119,8 +119,7 @@ \subsection{Impulse Response}
 	\begin{equation}
 	  x[n] = 4 + \sin[0.25\pi(n-1)] - 3 \sin[(2\pi/3)n]  
 	\end{equation}
-        You will need to start with multiple AnalogSignals and sample
-        them. Include a listing of your Matlab code and a figure with
+        Include a listing of your Matlab code and a figure with
         plots of the filter input and output in your report. Is the
         result expected? Why or why not?
 

Matlab Labs/lab5/lab5.tex

@@ -70,7 +70,7 @@ \subsection{Feedback Filters as Recurrence Relations}
 \end{equation}
 and we will get the Fibonacci sequence \emph{if} we input an impulse
 (hence, the appearance of the $x[n]$ on the right hand side, which
-serves only to initialize the filter). In Matlab, this can be don
+serves only to initialize the filter). In Matlab, this can be done
 trivially by taking a vector of all zeros --- let's call this vector
 \verb|x| --- and setting its first value only (\verb|x(1)|) to
 $C$. This is also a very good demonstration of the first ``I'' in the

Matlab Labs/lab6/lab6.tex

@@ -51,7 +51,7 @@ \subsection{Sound and images in MATLAB}
   works}.
 
 Within MATLAB, audio is a 1-D vector (stereo is $n \times 2$, but we
-won't deal with stereo) and grey-scale images are 2D arrays (color
+won't deal with stereo) and gray-scale images are 2D arrays (color
 images are 3-D arrays). For simplicity's sake, make sure any sound
 files you use are mono.
 
@@ -61,12 +61,12 @@ \subsubsection{Data Types}
 functions return often depends on the kind of file read. Regardless,
 almost all of the MATLAB functions you'll use to process data return
 doubles. For example, consider the following commands that read a
-color image, convert it to grey-scale, and display it:
+color image, convert it to gray-scale, and display it:
 \begin{lstlisting}[style=Matlab-editor,basicstyle=\mlttfamily\small]
 >> A = imread('/tmp/ariel.jpg');
 >> B = mean(A,3);
 >> imagesc(B)
->> colormap(grey)
+>> colormap(gray)
 >> axis equal
 >> whos
   Name      Size                           Bytes  Class
@@ -77,7 +77,7 @@ \subsubsection{Data Types}
 The (color) image is read into \verb|A|, which, as you can see from
 the output of the \verb|whos| command, is a 100x55x3 unsigned, 8-bit
 integer array (the third dimension for the red, green, and blue image
-color components). I convert the image to grey-scale by taking the
+color components). I convert the image to gray-scale by taking the
 mean of the three colors at each pixel (the overall brightness),
 producing a \verb|B| array that is \verb|double|. The
 \verb|imagesc| function displays the image, the \verb|colormap|
@@ -115,7 +115,7 @@ \subsection{Lossless image coding}
 (black-and-white).
 
 \paragraph{Step 1.1} Write a MATLAB script to read an image in,
-convert it to grey-scale if the image array is 3-D, and scale the
+convert it to gray-scale if the image array is 3-D, and scale the
 image values so they are in the range [1, 255] (note the absence of
 zero).  Verify that this has worked by using the \verb|min| and
 \verb|max| functions. Convert the results to \verb|uint8| and
@@ -217,21 +217,21 @@ \subsection{Lossy image coding: JPEG}
 
 \paragraph{Step 3.1} In this sequence of steps, we will use
 frequency-dependent quantization, similar to that used in JPEG, to
-compress an image. Start with your grey-scale, continuous-tone image
-from step 1.1 (if you used a color image, convert it to grey-scale as
+compress an image. Start with your gray-scale, continuous-tone image
+from step 1.1 (if you used a color image, convert it to gray-scale as
 you did in step 1.1). The MATLAB image processing or signal processing
 toolboxes are needed to have access to DCT functions, so we'll use the
 \verb|fft2()| and \verb|ifft2()| functions instead. To do a basic test
 of these functions, write a script that loads your image, converting
-it to grey-scale if necessary, and then computes its 2D FFT using
+it to gray-scale if necessary, and then computes its 2D FFT using
 \verb|fft2()|. The resulting matrix has complex values, which we will
 need to preserve. Display the magnitude of the FFT (remember to use
 the \verb|abs| function to get the magnitude of a complex number)
 using \verb|imagesc()|. Do this for each image type.  Can you relate
 any features in the FFT to characteristics in the original image?
 
 \paragraph{Step 3.2} Use \verb|ifft2()| to convert the FFT back and
-plot the result versus the original greyscale image (use
+plot the result versus the original gray-scale image (use
 \verb|imagesc()|) to check that everything is working fine. Analyze
 the difference between the two images (i.e., actually subtract them)
 to satisfy yourself that any changes are merely small errors