Can anybody suggest me to draw a more meaningful histogram? Or how can I get the opposite histogram of this bar plot?

I've some data distributions w.r.t a variable. I've plotted the histogram in the following way. Do I get more meaningful histogram if the change the axis ? Can anybody suggest me in this regards? Thanks and regards in advance.

xx=[1	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200	210	220	230	240	250];
K40=[0.4262	0.4313	0.4253	0.4278	0.8554	0.4206	0.426	0.4187	0.4255	0.858	0.8517	0.4257	0.8567	0.4288	0.8488	0.4265	0.8587	0.4183	0.4201	0.4278	0.8572	0.4251	0.4263	0.4291	0.4295	0.4303];
K82=[0.9941	0.8707	0.5442	0.9709	0.5538	0.7029	1.028	0.5364	0.7049	0.5278	0.5341	0.5141	0.8712	0.902	0.9365	0.5382	0.5316	0.9737	0.693	0.9925	0.532	0.9365	1.251	0.9374	0.5504	0.5298];
K152=[0.7171	0.7203	0.7256	0.7197	0.7258	0.7269	0.7132	0.7129	0.6941	0.7257	0.7131	0.7059	0.7191	0.7106	1.012	0.7141	0.7259	0.7182	0.9928	0.7104	0.7136	0.9859	1.001	0.712	0.7045	0.7184];
%% Making the Bar Plot Histogram 
p = [K40;K82;K152];
p=p';
figure; bar(p); 
title("Bar Histogram");
xlabel("100sec stretches of Data"); ylabel("KK distribution");
xticks(1:1:26);
xticklabels({'1st','10th','20th','30th','40th','50th','60th','70th','80th','90th','100th','110th','120th','130th','140th','150th','160th','170th','180th','190th','200th','210th','220th','230th','240th','250th'})
legend('Distribution of K@40Hz','Distribution of K@82Hz','Distribution of K@152Hz')

Answer 1

[William Rose]

@Sk. Alam, When I run your code I get the plot below. The triples of adjcent bars are hard to discern or appreciate. The x-xis labels overlap and are unreadable.

It is easier to perceive the differences between frequencies 40, 82, and 152 kHz by making three bar charts or by plotting three x,y sets on one plot, as shown by the following two figures. I lso djusted the labels to minimize overlap.

I have quesitons about the data. Are these really histograms? What is causing the quantization effects? Are the distributions different? Do these represent about 8 hours of data (100 sec x 250)?

1.Thee bar charts

2.Three sets of x,y on a single plot

Code for the above: attached.

[SA]

Thanks for your attempt. I've tried earlier for the figure 2 with the following scripts:

h=figure; grid on; hold on;
plot(xx,K40, 'LineStyle','-.', 'Color', 'b','linewidth', 1.35); 
plot(xx,K82, 'LineStyle','--', 'Color', 'r','linewidth', 1.35);
plot(xx,K152, 'LineStyle',':', 'Color', 'm','linewidth', 1.35);
xlim([0 250]); xticks(0:10:250);
ylim([0.3 1.3]); yticks(0.3:.1:1.3);
title(sprintf ('Distribution of K for 250 times 100s stretches of data'));
xlabel('Serial No.'); %,'FontSize',08,'FontWeight','bold');
ylabel('Magnitude of K'); %,'FontSize',08,'FontWeight','bold');
legend('Distribution of K@40Hz','Distribution of K@82Hz','Distribution of K@152Hz')
set(gcf, 'PaperUnits','inches','PaperPosition',[0 0 6.3 4]);
fig_name = ('Distribution_K');
ax = gca; ax.FontSize = 6; %ax.FontWeight = 'bold'; 
print(h,fig_name,'-dpng','-r2000'); 

"Are these really histograms?"

-I just want to check if histogram provides better visualization

"What is causing the quantization effects? "

I don't get your question at this point!!

Are the distributions different?

The value of K is different for 3 different frequencies @40Hz, @82Hz & @152Hz

Do these represent about 8 hours of data (100 sec x 250)?

No, It's not about 8hours of data; say xx=1 means for the first 100sec data bin I've calculate the value of K @40Hz, @82Hz & @152Hz are 0.4262, 0.9941 & 0.7171 respectively,

for xx=10 means at the 10-th instant of 100sec data bin I've calculate the value of K @40Hz, @82Hz & @152Hz are 0.4313, 0.8707 & 0.7203 respectively, and so on.

One thing I've in my mind is that is there any way to plot the same bar plot by altering the x- & y-axis? I don't understand how to alter the axis for that plotting/histogram. Thank you again.

Answer 2

[William Rose]

@Sk. Alam,

I still do not understand what you want to do. You said you are plotting the histograms, and that you want to get more meanigful histogram. However, it seems that you are plotting three time series: the K versus time at 40 Hz, at 82 Hz, and at 152 Hz. That is not a histogram. You said "xx=10 means at the 10-th instant of 100sec data bin I've calculate the value of K". You report values for xx which range from 1 to 250. Does this mean there are 250 "instants" in 100 seconds? Does one "instant" have a duration of 0.4 seconds?

A histogram is a plot of the number of times that a specific value occurs in a dataset, plotted versus the value. (Or it can be number of occurrences of values within specified bins, versus the bin center values.) This does not seem to be what you are plotting in your original bar chart. Matlab has a histo() function. If you want a histogram, why not use it? You could use it on your three data sets, or you could combine them and make a histogram of all 78 points.

What is K? Since K depends on frequency, I wonder if K corresponds to amplitude, or power, or phase, or time lag, or some other frequency-dependent property of a signal.

When I asked "What is causing the quantization effects?", I meant why do the K values cluster at specific levels, instead of being spread randomly across the range from lowest to highest K. Why do the values appear to be constrained to specific values or narrow ranges? Here is an actual histogram showing the frequency of different values of the elements of array p, which shows that the values of p are clustered at particular levels. This is what I mean by quantization. This plot was made as follows:

>> histogram([p(:,1);p(:,2);p(:,3)],[.3 .418 .432 .51 .555 .69 .73 .83 .85 .87 .89 .91 .93 .95 .97 1.03 1.24 1.26 1.3]);
>> xlabel('K'); ylabel('Frequency'); title('Histogram of p');

[SA]

@William Rose, thanks for your effort. Unfortunately, I don't understand this code; how do you get the value of qq ? Could you please explain?

qq=[.3 .418 .432 .51 .555 .69 .73 .83 .85 .87 .89 .91 .93 .95 .97 1.03 1.24 1.26 1.3];

"You report values for xx which range from 1 to 250"-- xx=[1 to 250], let's say 250 instants (if means 250 *100seconds of data, 100s data is not important here as I got K values from each 100s data bin) for each instant there are 100 seconds data from which I got the value of K. So, there should be 250 values of 'K' however, I've considered (for simplicity) 1,10,20,.....,250= 26 values of 'K'

"Does this mean there are 250 "instants" in 100 seconds? "-- There are 250 instants & every instant consider 100seconds of data.

"Does one "instant" have a duration of 0.4 seconds?"--NO

"What is K?"-- K is the value of wave number

"Since K depends on frequency"-- , Yes, K depends on frequency. For a specific frequency, K should be constant or slightly fluctuating (but in my case, I get abrupt fluctuations for several K values, I don't have control of getting K values as this depends on the 100s data). Thanks again for your patience.

[William Rose]

@Sk. Alam,

I chose the values of qq by hand, by inspecting the values in p, after concatenating the three columns into one, and then sorting the values. I then chose the values in qq to highlight the clustering of the values, to illustrate my point about quantiztion of the wavenumbers. It is not the proper way to do a histogram, but I was just tryiing to illustrate a point. A more proper way to do a hitogram is t oselect equal bin widths that give a balance between resolution and counts that is meaningful to you. Matlab's histogram will make default choices if you do not specify bin widths, and you can override those choices if you wish. See the documentation on histogram() for more details.

You said each instant is 100 s of data, and there are 250 instants. This is why I said earlier that this represents 8 hours of data - but you said it is not 8 hours - so I am confused. 100 seconds x 250 = 25000 seconds which is approximately 8 hours.

Thank you for explaining that K is wavenumber. I should have thought of that.

[SA]

Thanks for your explanation. I'm worried that I could find the value of 'qq' can you help me to find the 'qq' values as concatenating 3 columns gives 76 elements while qq has just 19 elements!! However, the result I got with the following scripts (slight changes with your scripts) is inclined with my expectation. I'll be happy if you explain 'qq' a bit more.

N.B.: ohh, yes, 100s*250=~ 7 hours of data is considered here.

Thanks & regards, SA

figure;
qq=[.3 .418 .432 .51 .555 .69 .73 .83 .85 .87 .89 .91 .93 .95 .97 1.03 1.24 1.26 1.3];
subplot(4,1,1); histogram(p(:,1),qq); grid on;
title("Histogram: K@40Hz");
ylabel("No. of DataBin");
subplot(4,1,2); histogram(p(:,2),qq); grid on;
title("Histogram: K@82Hz");
ylabel("No. of DataBin");
subplot(4,1,3); histogram(p(:,3),qq); grid on;
title("Histogram: K@152Hz");
ylabel("No. of DataBin");
subplot(4,1,4);
histogram(p(:,1),qq); hold on; grid on
histogram(p(:,2),qq); histogram(p(:,3),qq);
xlabel('Distribution of K'); ylabel('No. of 100s Data Bin'); title('Combined Histogram of 3 Freq');
legend('Dist. of K@40Hz','Dist. of K@82Hz','Dist. of K@152Hz')

[William Rose]

@Sk. Alam, The number of elements in qq may be more than or less than or equal to the number of elements in p or in p(:,i). qq specifies the edges of the bins, i.e. the x-axis coordinates for the histogram plot. The attached code illustrates how the choice of qq influences the histogram. The values I chose for this example are arbitrary. There are no "right" or "wrong" values for qq, except the values should at least span the min and max of the data set. It depends on what you want to do with this histogram, or what point you wish to illustrate. I don't know exactly how Matlab chooses the default bins, but I do know that the number of default bins gets larger (i.e. bins get more narrow) when the number of values in the data set gets larger.

>> figure;
>> subplot(3,1,1);
>> histogram(pall);
>> title('Matlab default bins');
>> qq=0.4:.05:1.3;
>> subplot(3,1,2);
>> histogram(pall,qq);
>> title('Bin edges 0.4:.05:1.3');
>> qq=0.2:.02:1.5;
>> subplot(3,1,3);
>> histogram(pall,qq);
>> title('Bin edges 0.2:.02:1.5');

The code above generates the figure below.

Here is another example of histogram with default bins. In this cae, the data set is 1000 normal random numbers. Code, then figure.

>> rands=randn(1000,1);
>> figure;
>> histogram(rands)

Figure made by code above.