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Digital Telephony By John Bellamy Solution Manual Page

“You’ve learned more tonight than any solution manual could teach you,” Bellamy said. “Now throw it away. Redo the problems. And when you’re done, mail me your own solutions. I’ll grade them myself.”

In the late 1990s, a frazzled graduate student named Mira was buried under a mountain of signal processing equations. Her digital communications professor had assigned the legendary—and notoriously dense—textbook Digital Telephony by John Bellamy. The problem sets were brutal: convolution, quantization noise, T1 framing, and echo cancellers that seemed to work only in theory.

She did. A month later, she received a postcard: “Grade: A. Welcome to digital telephony.”

The next day, a strange thing appeared in her department mailbox. A plain manila envelope, no return address, containing a photocopied, spiral-bound booklet. On the cover, handwritten in blue ink: “Bellamy – Solutions – Not for distribution.” digital telephony by john bellamy solution manual

Mira’s heart raced. She flipped through it. There it was: Problem 4.17, the one about adaptive differential PCM that had made her cry two nights ago. Step-by-step derivations. Elegant. Complete.

She tracked down John Bellamy’s office number and called. An older, kind voice answered. “Ah,” he said after she explained. “You found my little trap. I plant those solution manuals for the desperate. But here’s the secret: the real solution manual is working through each problem until you understand it well enough to spot my intentional error on page 73.”

And from that day on, Mira never looked for a shortcut again—only for the sign error that proved she truly understood. “You’ve learned more tonight than any solution manual

Mira flipped to page 73 of the photocopied manual. Problem 5.2’s answer was subtly off by a sign. She had copied it without thinking.

One evening, in the bowels of the engineering library, Mira whispered a quiet prayer to the gods of Nyquist and Shannon. “If only I had the solution manual,” she muttered.

She used it sparingly at first—just to check her work. But soon, the temptation grew. She began copying verbatim. Her homework became flawless. Her professor pulled her aside. “Mira, this is stunning. You have a real future in telephony.” And when you’re done, mail me your own solutions

But guilt gnawed at her. One night, she noticed a small detail in the solution manual: a tiny handwritten note in the margin beside a root-finding problem. It read: “This was the only problem John got wrong in the first edition. Fix in 2nd printing.”

Mira froze. She checked her library’s first edition of Digital Telephony . The problem statement matched. But the correction? Only someone intimately connected to Bellamy—perhaps the author himself—would know that.

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SPSS Statistics

SPSS Statistics procedure to create an "ID" variable

In this section, we explain how to create an ID variable, ID, using the Compute Variable... procedure in SPSS Statistics. The following procedure will only work when you have set up your data in wide format where you have one case per row (i.e., your Data View has the same setup as our example, as explained in the note above):

  1. Click Transform > Compute Variable... on the main menu, as shown below:

    Note: Depending on your version of SPSS Statistics, you may not have the same options under the Transform menu as shown below, but all versions of SPSS Statistics include the same compute variable menu option that you will use to create an ID variable.

    computer menu to create a new ID variable

    Published with written permission from SPSS Statistics, IBM Corporation.


    You will be presented with the Compute Variable dialogue box, as shown below:
    'recode into different variables' dialogue box displayed

    Published with written permission from SPSS Statistics, IBM Corporation.

  2. Enter the name of the ID variable you want to create into the Target Variable: box. In our example, we have called this new variable, "ID", as shown below:
    ID variable entered into Target Variable box in top left

    Published with written permission from SPSS Statistics, IBM Corporation.

  3. Click on the change button and you will be presented with the Compute Variable: Type and Label dialogue box, as shown below:
    empty 'compute variable: type and label' dialogue box

    Published with written permission from SPSS Statistics, IBM Corporation.

  4. Enter a more descriptive label for your ID variable into the Label: box in the –Label– area (e.g., "Participant ID"), as shown below:
    participant ID entered in 'compute variable: type and label' dialogue box

    Published with written permission from SPSS Statistics, IBM Corporation.

    Note: You do not have to enter a label for your new ID variable, but we prefer to make sure we know what a variable is measuring (e.g., this is especially useful if working with larger data sets with lots of variables). Therefore, we entered the label, "Participant ID", into the Label: box. This will be the label entered in the label column in the Variable View of SPSS Statistics when you complete at the steps below.

  5. Click on the continue button. You will be returned to the Compute Variable dialogue box, as shown below:
    ID variable entered

    Published with written permission from SPSS Statistics, IBM Corporation.

  6. Enter the numeric expression, $CASENUM, into the Numeric Expression: box, as shown below:
    second category - '2' and '4' - entered

    Published with written permission from SPSS Statistics, IBM Corporation.

  7. Explanation: The numeric expression, $CASENUM, instructs SPSS Statistics to add a sequential number to each row of the Data View. Therefore, the sequential numbers start at "1" in row 1, then "2" in row 2, "3" in row 3, and so forth. The sequential numbers are added to each row of data in the Data View. Therefore, since we have 100 participants in our example, the sequential numbers go from "1" in row 1 through to "100" in row 100.

    Note: Instead of typing in $CASENUM, you can click on "All" in the Function group: box, followed by "$Casenum" from the options that then appear in the Functions and Special Variables: box. Finally, click on the up arrow button. The numeric expression, $CASENUM, will appear in the Numeric Expression: box.

  8. Click on the ok button and the new ID variable, ID, will have been added to our data set, as highlighted in the Data View window below:

data view with new 'nominal' ID variable highlighted

Published with written permission from SPSS Statistics, IBM Corporation.


If you look under the ID column in the Data View above, you can see that a sequential number has been added to each row, starting with "1" in row 1, then "2" in row 2, "3" in row 3, and so forth. Since we have 100 participants in our example, the sequential numbers go from "1" in row 1 through to "100" in row 100.

Therefore, participant 1 along row 1 had a VO2max of 55.79 ml/min/kg (i.e., in the cell under the vo2max column), was 27 years old (i.e., in the cell under the age column), weighed 70.47 kg (i.e., in the cell under the weight column), had an average heart rate of 150 (i.e., in the cell under the heart rate column) and was male (i.e., in the cell under the gender column).

The new variable, ID, will also now appear in the Variable View of SPSS Statistics, as highlighted below:

variable view for new 'nominal' ID variable highlighted

Published with written permission from SPSS Statistics, IBM Corporation.


The name of the new variable, "ID" (i.e., under the name column), reflects the name you entered into the Target Variable: box of the Compute Variable dialogue box in Step 2 above. Similarly, the label of the new variable, "Participant ID" (i.e., under the label column), reflects the label you entered into the Label: box in the –Label– area in Step 4 above. You may also notice that we have made changes to the decimals, measure and role columns for our new variable, "ID". When the new variable is created, by default in SPSS Statistics the role column will be set to "2" (i.e., two decimal places), the measure will show scale and the role column will show input. We changed the number of decimal places in the decimals column from "2" to "0" because when you are creating an ID variable, this does not require any decimal places. Next, we changed the variable type from the default entered by SPSS Statistics, scale, to nominal, because our new ID variable is a nominal variable (i.e., a nominal variable) and not a continuous variable (i.e., not a scale variable). Finally, we changed the cell under the role from the default, input, to none, for the same reasons mentioned in the note above.

Referencing

Laerd Statistics (2025). Creating an "ID" variable in SPSS Statistics. Statistical tutorials and software guides. Retrieved from https://statistics.laerd.com/


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