Interactive exploration · Synthetic data

When does a signal become unusual?

Explore the mathematics behind anomaly detection. Change a threshold and watch the tradeoff between sensitivity and false alarms.

Detection threshold 0.35 Inject anomalies

Reference and observed signal

240 synthetic samples. The known reference is a sine wave; deterministic noise and optional spikes/burst produce the observed signal.

— Observed┄ Reference○ Detected

10 detected samples at the default threshold.

Detected samples10

True positives10

False positives0

Missed anomalies0

The mathematical rule

|observed − reference| > threshold

A lower threshold catches smaller deviations, including ordinary noise. A higher threshold ignores more noise but can miss genuine anomalies. Counts refer to samples, not separate incidents.

The injected ground truth contains two isolated spikes and an eight-sample burst. Turning injection off makes every detection a false positive.

From electronics to AI

I enjoy understanding patterns, reasoning through uncertainty, and connecting mathematical ideas to systems we can inspect. Signals offer a direct connection between my electronics background and my curiosity about AI.

This experiment uses a threshold rule, not a trained AI model. A learned model could estimate expected behavior when a clean reference is unavailable. That introduces new questions about training data, drift, evaluation, and uncertainty.

Inspect all 240 samples

Sample	Reference	Observed	Injected anomaly	Detected
0	0.000	0.040	No	No
1	0.105	0.201	No	No
2	0.208	0.303	No	No
3	0.309	0.338	No	No
4	0.407	0.346	No	No
5	0.500	0.384	No	No
6	0.588	0.487	No	No
7	0.669	0.643	No	No
8	0.743	0.800	No	No
9	0.809	0.904	No	No
10	0.866	0.934	No	No
11	0.914	0.919	No	No
12	0.951	0.907	No	No
13	0.978	0.932	No	No
14	0.995	0.989	No	No
15	1.000	1.036	No	No
16	0.995	1.034	No	No
17	0.978	0.974	No	No
18	0.951	0.890	No	No
19	0.914	0.830	No	No
20	0.866	0.820	No	No
21	0.809	0.843	No	No
22	0.743	0.846	No	No
23	0.669	0.781	No	No
24	0.588	0.639	No	No
25	0.500	0.460	No	No
26	0.407	0.303	No	No
27	0.309	0.208	No	No
28	0.208	0.170	No	No
29	0.105	0.141	No	No
30	0.000	0.072	No	No
31	-0.105	-0.053	No	No
32	-0.208	-0.209	No	No
33	-0.309	-0.347	No	No
34	-0.407	-0.436	No	No
35	-0.500	-0.483	No	No
36	-0.588	-0.531	No	No
37	-0.669	-0.617	No	No
38	-0.743	-0.747	No	No
39	-0.809	-0.882	No	No
40	-0.866	-0.970	No	No
41	-0.914	-0.982	No	No
42	-0.951	-0.934	No	No
43	-0.978	-0.882	No	No
44	-0.995	-0.877	No	No
45	-1.000	-0.932	No	No
46	-0.995	-1.013	No	No
47	-0.978	-1.062	No	No
48	-0.951	-1.040	No	No
49	-0.914	-0.952	No	No
50	-0.866	-0.842	No	No
51	-0.809	-0.757	No	No
52	-0.743	-0.714	No	No
53	-0.669	-0.687	No	No
54	-0.588	-0.632	No	No
55	-0.500	-0.523	No	No
56	-0.407	-0.373	No	No
57	-0.309	-0.230	No	No
58	-0.208	-0.136	No	No
59	-0.105	-0.096	No	No
60	-0.000	-0.073	No	No
61	0.105	-0.012	No	No
62	0.208	0.119	No	No
63	0.309	0.303	No	No
64	0.407	0.486	No	No
65	0.500	0.612	No	No
66	0.588	0.662	No	No
67	0.669	0.668	No	No
68	0.743	0.682	No	No
69	0.809	0.741	No	No
70	0.866	2.240	Yes	Yes
71	0.914	0.938	No	No
72	0.951	0.991	No	No
73	0.978	0.987	No	No
74	0.995	0.954	No	No
75	1.000	0.939	No	No
76	0.995	0.966	No	No
77	0.978	1.018	No	No
78	0.951	1.047	No	No
79	0.914	1.008	No	No
80	0.866	0.895	No	No
81	0.809	0.748	No	No
82	0.743	0.627	No	No
83	0.669	0.568	No	No
84	0.588	0.562	No	No
85	0.500	0.557	No	No
86	0.407	0.501	No	No
87	0.309	0.377	No	No
88	0.208	0.213	No	No
89	0.105	0.060	No	No
90	0.000	-0.046	No	No
91	-0.105	-0.110	No	No
92	-0.208	-0.172	No	No
93	-0.309	-0.269	No	No
94	-0.407	-0.410	No	No
95	-0.500	-0.561	No	No
96	-0.588	-0.671	No	No
97	-0.669	-0.715	No	No
98	-0.743	-0.709	No	No
99	-0.809	-0.706	No	No
100	-0.866	-0.754	No	No
101	-0.914	-0.862	No	No
102	-0.951	-0.991	No	No
103	-0.978	-1.082	No	No
104	-0.995	-1.095	No	No
105	-1.000	-1.038	No	No
106	-0.995	-0.958	No	No
107	-0.978	-0.906	No	No
108	-0.951	-0.900	No	No
109	-0.914	-0.915	No	No
110	-0.866	-0.904	No	No
111	-0.809	-0.838	No	No
112	-0.743	-0.727	No	No
113	-0.669	-0.612	No	No
114	-0.588	-0.536	No	No
115	-0.500	-0.504	No	No
116	-0.407	-0.480	No	No
117	-0.309	-0.413	No	No
118	-0.208	-0.276	No	No
119	-0.105	-0.088	No	No
120	-0.000	0.796	Yes	Yes
121	0.105	0.923	Yes	Yes
122	0.208	0.976	Yes	Yes
123	0.309	0.991	Yes	Yes
124	0.407	1.023	Yes	Yes
125	0.500	1.111	Yes	Yes
126	0.588	1.249	Yes	Yes
127	0.669	1.393	Yes	Yes
128	0.743	0.795	No	No
129	0.809	0.838	No	No
130	0.866	0.848	No	No
131	0.914	0.869	No	No
132	0.951	0.929	No	No
133	0.978	1.012	No	No
134	0.995	1.074	No	No
135	1.000	1.072	No	No
136	0.995	1.003	No	No
137	0.978	0.905	No	No
138	0.951	0.835	No	No
139	0.914	0.825	No	No
140	0.866	0.860	No	No
141	0.809	0.888	No	No
142	0.743	0.855	No	No
143	0.669	0.744	No	No
144	0.588	0.587	No	No
145	0.500	0.439	No	No
146	0.407	0.338	No	No
147	0.309	0.283	No	No
148	0.208	0.232	No	No
149	0.105	0.144	No	No
150	0.000	0.009	No	No
151	-0.105	-0.145	No	No
152	-0.208	-0.269	No	No
153	-0.309	-0.338	No	No
154	-0.407	-0.367	No	No
155	-0.500	-0.404	No	No
156	-0.588	-0.493	No	No
157	-0.669	-0.640	No	No
158	-0.743	-0.804	No	No
159	-0.809	-0.925	No	No
160	-0.866	-0.967	No	No
161	-0.914	-0.940	No	No
162	-0.951	-0.894	No	No
163	-0.978	-0.884	No	No
164	-0.995	-0.926	No	No
165	-1.000	-0.995	No	No
166	-0.995	-1.039	No	No
167	-0.978	-1.024	No	No
168	-0.951	-0.957	No	No
169	-0.914	-0.877	No	No
170	-0.866	-1.926	Yes	Yes
171	-0.809	-0.813	No	No
172	-0.743	-0.804	No	No
173	-0.669	-0.753	No	No
174	-0.588	-0.634	No	No
175	-0.500	-0.466	No	No
176	-0.407	-0.304	No	No
177	-0.309	-0.197	No	No
178	-0.208	-0.157	No	No
179	-0.105	-0.145	No	No
180	-0.000	-0.104	No	No
181	0.105	0.004	No	No
182	0.208	0.170	No	No
183	0.309	0.345	No	No
184	0.407	0.479	No	No
185	0.500	0.551	No	No
186	0.588	0.587	No	No
187	0.669	0.631	No	No
188	0.743	0.714	No	No
189	0.809	0.826	No	No
190	0.866	0.923	No	No
191	0.914	0.965	No	No
192	0.951	0.947	No	No
193	0.978	0.905	No	No
194	0.995	0.890	No	No
195	1.000	0.932	No	No
196	0.995	1.011	No	No
197	0.978	1.074	No	No
198	0.951	1.069	No	No
199	0.914	0.982	No	No
200	0.866	0.848	No	No
201	0.809	0.725	No	No
202	0.743	0.654	No	No
203	0.669	0.631	No	No
204	0.588	0.612	No	No
205	0.500	0.552	No	No
206	0.407	0.436	No	No
207	0.309	0.291	No	No
208	0.208	0.164	No	No
209	0.105	0.082	No	No
210	0.000	0.034	No	No
211	-0.105	-0.025	No	No
212	-0.208	-0.136	No	No
213	-0.309	-0.301	No	No
214	-0.407	-0.480	No	No
215	-0.500	-0.616	No	No
216	-0.588	-0.677	No	No
217	-0.669	-0.675	No	No
218	-0.743	-0.664	No	No
219	-0.809	-0.697	No	No
220	-0.866	-0.791	No	No
221	-0.914	-0.915	No	No
222	-0.951	-1.012	No	No
223	-0.978	-1.046	No	No
224	-0.995	-1.021	No	No
225	-1.000	-0.976	No	No
226	-0.995	-0.955	No	No
227	-0.978	-0.970	No	No
228	-0.951	-0.991	No	No
229	-0.914	-0.975	No	No
230	-0.866	-0.895	No	No
231	-0.809	-0.769	No	No
232	-0.743	-0.647	No	No
233	-0.669	-0.575	No	No
234	-0.588	-0.559	No	No
235	-0.500	-0.561	No	No
236	-0.407	-0.523	No	No
237	-0.309	-0.410	No	No
238	-0.208	-0.234	No	No
239	-0.105	-0.048	No	No