Transcript Objectives: By the end of this class you should be able to:

Descriptive Statistics I:
By the end of this class you should be able to:
•
Program cords and delays in your music programs
•
plot a histogram of absolute frequencies and
describe its nature
vary the number of bins in a histogram and choose an
appropriate number
plot a histogram of relative frequencies and explain
why it is needed.
•
•
Palm: Section 7.1, 7.2
Practice Problem (groups of 3):
A debugging a Sine Series Function
• The sin function can be approximated by the series:
k *21
n
x3 x5
x
sin( x)  x  
   (1) k 1
3! 5!
(k * 2  1)!
k 1
• Download the function: SinSeries1.m from the website
• This function was developed to estimate the sine using
the above series given the x-value and n, the number of
terms to be used in the sequence.
• Follow the instructions on the worksheet handout.
function S =
SinSeries(x,n)
Flowchart for Sine
Series Problem
Calculate first term
S=x
Done with
index array
for terms 2
through n
S = S + new term
End
Working with Chords
download “chordplay.m” from the “Music in MATLAB’ page
Open this script in the MATLAB editor.
Exercise instructions and questions are in the comments of this script.
Please write down answers to these questions.
To “uncomment” remove the “%” from the beginning of a line
Exercises 1: Play a major chord
1. What are the names for these three notes?
2. What advantage can you see to calculating them this way
instead of just typing in the frequencies?
3. How are the three note series combined into one
series/chord.
Exercise 2: Add a delay
4. How is the delay created?
5. Why is the pad added at the end of the first note twice?
6. What are the dimensions of the chord array?
Exercise 3: Play two notes in stereo
7. What are the dimensions of the chord array now?
Saving and Loading .wav files
•
Loading .wav files:
>> [series, sf, bits] = wavread(‘wavfile’)
•
Saving a .wav:
>> wavwrite (series, sf, bits, ‘filename’)
•
Import Wizard: File  Import Data
Characteristics of a stored ware
1
Series: The list of yvalues for the wave.
0.8
0.6
Sampling Frequency:
how many times per
second you have a data
point = 1/(interval
between points)
0.4
amplitude
0.2
0
-0.2
Bits: The number of
significant figures used
in the y-values (in binary)
-0.4
-0.6
8 bits = 256 levels
16 bits = 65,536 levels
24 bits = 16 x 106 levels
-0.8
-1
0
0.5
1
1.5
time(sec.)
2
2.5
-3
x 10
Descriptive Statistics
please download cordbreak1.mat
& load into MATLAB
Palm: Section 7.1, 7.2
Histogram: a frequency plot
>> hist(cord)
>> xlabel 'breaking force (N)'
>> ylabel 'absolute frequency'
Histogram Bins
• Bins can greatly effect the look of a histogram
• By default MATLAB uses 10 bins
• Adjusting bins in MATLAB:
>> hist(cord, n)
where n is the number of bins desired
• Exercise: Create a figure with four plots arranged
2x2 where the plots are histograms of the cordbreak
data with bin numbers of 10, 20, 5 and 7.
Histogram Commands
>> hist (data)
 histogram with 10 equal width bins
>> hist(data, number of bins)
 histogram with specified number of bins
>> [z, x] = hist(data)
 no histogram produced
 outputs a vector of heights (z) and
the center point of each bin (x)
try using this command. Then try
>> bar(x, z)
>> hist(data, vector of bin centers)
 bins are centered at the provided values
Relative Frequency Histogram
•
Try this:
>> [z,x]=hist(cord);
>> zr=z/sum(z)
>> bar(x,zr)
add axis labels etc.
•
Frequency is relative to the total number of
samples (N). Each bar is the fraction of
samples in that bin
•
This histogram is independent of total sample
size
Formula
MATLAB
EXCEL
>> mean(variable)
= average(range)
>> std(variable)
= stdev(range)
n
Mean
Sample
Standard
Deviation
x
x 
i 1
i
n
n
sx 
2
(
x

x
)
 i
i 1
n 1