MI 3110 Recording Techniques I

MI 3110 – Recording Techniques I Answer Key

Midterm Examination

Wednesday, October 18, 2000

Use separate sheets as necessary – please write your name on each!

Part I: Graphics

1. Write a short description of each of these paired graphics: (a,b); (c,d); (e,f) and (g,h). (4 points)

1.  (a,b) One complete cycle of a sine wave in TDR and FDR graphic representations. Only the fundamental frequency is shown in the FDR since no overtones are present.

2.  (c,d) One complete cycle of a sawtooth wave in TDR and FDR. This wave has a rich complement of overtones as described in the FDR. They tend to drop-off in amplitude exponentially.

3.  (e,f) A more complex waveform which is not as clearly periodic as the first two in TDR form. The FDR shows various frequencies which are equal in loudness. These are harmonics that might be heard as formants. Note that the FDR also shows very low-level spectral energy between the louder partials.

4.  (g,h) The most complex signal depicted, and most probably aperiodic, according to the TDR. The FDR is abbreviated through the omission of spectral components 42-211. This is done to save space. What is described in the FDR is a spectrum of relatively uniform energy distribution on either side of the omitted area. By considering the lower part of the spectrum in comparison to the upper part of the spectrum (in addition to the uncorrelated nature of the TDR waveform) it becomes possible to suggest that this is an example of low-passed noise – the high frequencies in the FDR are attenuated in level.

2. Describe the facts of this signal by considering the TDR and FDR representations. (1 point)

This pairing of TDR and FDR shows a signal which has both harmonic and inharmonic attributes. In fact, this is quite common in complex and interesting sounds that we may wish to record. The FDR is given first and has a 200Hz fundamental and a signal which is harmonically related (integer multiple) at 2000Hz. Two other frequencies 347.5Hz and 9921.8Hz are shown which are inharmonic, both to each other and to the previously mentioned harmonically related frequencies. The TDR is appropriate to the context described in the FDR as it shows a very strong sinusoidal fundamental component and also higher frequencies in the signal at highly attenuated amplitude levels.

3. This graphic describes a specific process of signal development by addition, what is the process and the result? (1 point)

This graphic shows the evolution from simple sinusoidal shape to a nearly complete square through a simple process of waveform addition. In (b) a frequency 1/3 that of (a) is added at an amplitude level of 1/3 (one over the harmonic number). Note that the frequencies are integer related and thus harmonic. In (c) the frequency added to the sine is 1/5 that of (a) and the amplitude is yet smaller at 1/5. In (d) the frequency added is 1/9 of (a) and the amplitude is 1/9.

The result of adding many of these elements together and according to the rule described is shown in (e), it is a square wave.

4. The following two graphics are associated with a specific parameter of sound waves. What is this property and what are the implications for audio recording and playback? (1 point)

These two graphics deal with the parameter of phase, which is common in all complex signals and it an aspect of sonic richness when considered together with frequency and amplitude. Phase information is important in particular to a) timbre perception and evolution and also to b) auditory localization.

The answer to this question would describe the concept of phase in general terms, showing that the cosine phase is ¼ phase or 90Deg phase shift. The audible result will be constructive and destructive interference , that is the amplitudes add together in certain places and subtract from each other in others. This is shown dramatically in the second graphic where two waves of the same frequency and amplitude but opposite phase combine to create silence – they cancel each other out.

The implications for recording are many but the main ones we have discussed so far are that 1) phase shift can result in subtle timbral changes which are heard as anomalous boosts and cuts in the frequency spectrum of complex sounds and 2) out of phase information can compromise monaural compatibility of stereo recordings. It is therefore necessary to make sure when using multiple microphones to record in stereo that the distance between the microphones and the source follows (whenever possible) the 3:1 rule. The objective is to minimize out of phase information from the source in each microphone.

5. A spectral plot is another name for Frequency Domain Representation or FDR. Compare the following two spectral plots and the way they are presented graphically noting important difference and also similarities. (2 points)

Differences:

(a)  amplitude is a linear scale (y-axis), and integer-related partials are shown (x-axis) – therefore this is a harmonic sound.

(b)  amplitude is a logarithmic scale (dB) (y-axis) and frequency is graphed on the x-axis showing the appearance of inharmonic elements – on this TDR it is difficult to discern which elements are harmonically related, yet, the large peaks seem to be equally spaced in frequency (harmonic) and the frequency scale is apparently linear. There is much more detail in frequency in this FDR and obviously harmonic and inharmonic elements are both present.

Similarities:

(a)  both sounds are complex and have many partials in them

(b)  both FDRs are in 2 dimensions

(c) upper partials of both sounds have less energy than lower ones

6. When spectral plots are graphically described in three dimensions further important information is added. Explain in terms of the spectral plot given. What part of the sound is the loudest? What part of the sound lasts longest? (3 points)

Time-varying FDRs are perhaps the most important new tool for audio engineering. They combine several important elements into one graphic description and, with familiarity, become quite useful for the engineer in making subtle aspects of sound carefully nuanced.

Answer:

This FDR shows time on the z-axis. Therefore it is a 3-dimensional spectrum. It also shows 12 partials which are harmonically related and the amplitude of each evolves over time. The relative amplitudes of the partials drop-off as the partial number increases and the frequency becomes higher. Each partial has not only an individual amplitude peak, but also an individual amplitude envelope and therefore, an individually perceived duration.

The 3rd partial is the loudest and is possibly a formant, providing important coloration to the timbre of the tone analyzed and the first partial is the longest in duration.

7. This two-dimensional spectral plot, or FDR, shows some features of the sound depicted known as FORMANT regions or peaks. Mark these on the graphic. Why is this information potentially useful when applying equalization in the audio recording process? (3 points)

What is shown may be described as a magnitude spectrum. Rather that showing each specific partial in the sound, it shows a general energy distribution (size) over the number of partials up to about 3500Hz where the energy seems to be largely dissipated.

This information is useful because formant areas in sound spectra are important regions which provide the timbral “identity” for sounds. These are regions which impart specific qualities to sounds allowing them to be recognized as distinct from other sounds. For example, one person’s voice from another person’s voice, a violin from an oboe, a piano from a marimba and so on. Therefore, knowing about formant peaks in sounds becomes a valuable allay in helping you to shape frequency equalization using a console, choose appropriate microphones for recording sounds, select microphone placement techniques depending on characteristic of an instrument and apply digital signal processing techniques in an informed and scientifically sound manner.

8. Completely label these graphics. Describe in detail what they depict. (4 points)

This one is rather straight forward. For each of the graphics the appropriate labels should be applied. It would also be appropriate to label both the X and Y axes. Y will have linear amplitude and X linear frequency. For the bottom two both fc (center frequency) and BW need to be shown on the graphic.

These are the four basic filter types. Lowpass – passes low frequencies below the cut off frequency and attenuates high frequencies above. The Highpass filter does the opposite. The Bandpass filter describes a band of contiguous frequencies and allows them to be heard which attenuating frequencies outside of that band. The Bandreject of Notch filter does the opposite. Both of the latter two types use center frequency and bandwidth controls to define the passed or rejected bands.

One could go further to describe how the Lowpass and Highpass combine to create the Bandpass and Bandreject filters (using both serial and parallel models). It may also be noted that each of the basic filter types is capable of “total band rejection” or TBR.

9. Completely label these graphics. Describe in detail what they depict. (2 points)

These graphics describe a specific kind of filter found on many consoles in the EQ section. They are known as shelving filters (or shelving EQ). The top one is a “high shelf” the bottom one a “low shelf”. The top one is similar in action to a Lowpass filter, while the bottom one is similar in action to a Highpass filter. These units only affect frequencies after the cut-off frequency and will either boost or cut amplitude above or below this cut-off point. Further, the boost or cut is then constant (after the slope, which may be rather steep) for all frequencies beyond the cut-off to the ends of the audio bandwidth of the system. Therefore, an amplitude “shelf” is described by this unit and it will attenuate frequencies above of below the cut-off at a constant level which the user can describe as the boost or cut value.

As discussed in lecture, a high shevling EQ would be useful for attenuating unwanted high frequencies in a sound coming into a console line input – for example, tape hiss from a noisy recording. A low shelving EQ would be useful for attenuating low frequency rumble often found in rooms where recordings take place, or on location in the field.

These units add important functionality to an EQ unit and nearly all pro-level consoles have them. They free-up the other parameters of the EQ section and allow more articulate tools, such as parametric EQ bands, to be applied to important areas of the spectrum of the recorded sound.

(This is a bit long-winded, a simple answer identifying these units and their function is sufficient.)

10. The following formula describes an important relation used in audio filtering and equalization. What is it and what is it used for? Where on the Mackie Console can we find this concept applied? (2 points)

This is the formula for Q, or the “quality factor “of a filter or equalizer. Because frequency is geometrically expanding – an octave is a doubling of frequency – it is helpful to think about bandwidth in terms of Q rather than specific frequency values. In this way it is possible to know how to apply the same Q value (or bandwidth) for any specific frequency band and therefore describe constant Q equalization. As frequency increases so does bandwidth.

Answer:

Q or the quality factor of a filter or equalizer

High-Mid Band in the EQ section of the Mackie

(In fact, this is the only true parametric band on the Mackie 8-Bus. The Tascam 3700 in Studio B does not have one at all but only constant Q bands which boost and cut. The Yamaha O2R has 4 fully parametric bands. When consoles lack parametric bands it is possible to supplement them with outboard equipment. In studio B we have two sophisticated fully parametric equalizers which are possible to connect and use in conjunction with the 3700.)

Part II: Problems, Short Answers and Essayed Responses

Filtering: In making responses it is acceptable to use either a rectangle cutoff or a slope of –3dB/oct (for example).

11. A bandpass filter with a CF of 1000Hz and a Q of 5 (2 points)

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12. A bandpass filter with a BW of 1000Hz and a CF of 3500Hz (2 points)

13. A bandreject filter with a CF of 800 and a Q of 20 (2 points)

14. A bandreject filter with a CF of 1000 and BW of fc/100 (2 points)

15. Another name for a bandreject filter is a NOTCH filter because it rejects a specific band of the total spectrum and thereby takes chunk out of it.

16. The main difference between a filter and an equalizer is that a filter is a PASSIVE circuit and an equalizer is an ACTIVE one.

17. Equalizers differ from filters in that they

a.  boost or attenuate frequencies in band

b.  break up the total frequency band into controllable sub-bands

c.  can be shelving or parametric

d.  often use Q to describe bandwidth

e.  all of the above

18. A shelving equalizer is one which

a.  is usually put away until it is used

b.  is just like a lowpass filter

c.  attenuates highs or lows at a specific cut-off frequency but does not attenuate beyond a certain decibel level that is preset

d.  is nothing like your home stereo tone controls

e.  works regardless of input polarity or Q ratio settings

19. T / F Frequencies which are attenuated less than 3dB are said to be “inside the passband” and those attenuated by more than 3dB are said to be “outside the passband”.